东北大学matlab作业

1、Matlab 上机实验作业 第一部分：2.用MATLA语句输入矩阵A和B1234432123411 4j 2 3j4 1j 3 2j2 3j 3 2j3 2j 4 1j2 3j 1 4j4 1j 1 4j32413 2j 2 3j 4 1j 1 4j前面给出的是 4 4 矩阵，如果给出 A(5,6) 5命令将得出什么结果解 A=1,2,3,4;4,3,2,1;2,3,4,1;3,2,4,1A =1 2 3 44 3 2 12 3 4 13 2 4 1 b=1+4j 2+3j 3+2j 4+1j;4+1j 3+2j 2+3j 1+4j;2+3j 3+2j 4+1j 1+4j;3+2j 2+3j

2、4+1j 1+4jb =+ + + + + + + + + + + + + + + A(5,6)=5A =3假设已知矩阵 A ，试给出相应的MATLAB令，将其全部偶数行提取出来，赋123400432100234100324100000005给B矩阵，用A magic(8)命令生成A矩阵，用上述命令检验一下结果是不是正1解 A=magic(8)A =634用数值方法可以求出 S 2i 1i02 4 8 262 263 ，试不采用循环的642361606757955541213515016174746202143422440262737363031333234352928383925412322

3、44451918484915145253111056858595462631B=A(2:2:end,:)B =95554121351501640262737363031334123224445191848858595462631形式求出和式的数值解。由于数值方法是采用 double 形式进行计算的，难以保 证有效位数字，所以结果不一定精确。试采用运算的方法求该和式的精确值。 解 sum(sym(2)41:63)ans =9551615选择合适的步距绘制出下面的图形。(1) sin (1/t)，其中 t ( 1,1) ；(2) sin( ta nt) tan( si nt)，其中 t (,)解(

4、1) t=-1:1;y=sin(1./t);plot(t,y)4(2) x=-pi:,:,:,:,:pi;y=si n(ta n(x)-ta n(si n(x);plot(x,y)6.试绘制出二元函数zf(x, y)1(1 x)2 y21(1 x)2y2的三维图和三视图。解xx=-2:,:,:,:,:2;yy=-1:,:,:1;x,y=meshgrid(xx,yy);z=1./(sqrt(1-x).A2+y.A2)+1./(sqrt(1+x).A2+y.A2);surf(x,y,z),shading flat;zlim(0,15) xx=-2:,:,:,:,:2;yy=-1:,:,:1;z=1

5、./(sqrt(1-x).A2+y.A2)+1./(sqrt(1 +x).A2+y.A2);subplot(221),surf(x,y,z),view(0,90);subplot(222),surf(x,y,z),view(90,0);subplot(223),surf(x,y,z),view(0,0);150-11550-1ri_一I in Un105100-17.试求出如下极限。1(1) lim (3x 9x)x ;x(2) lim(3)1 cos(x2 limx 0y 0y2)(x2 y2)e y2解(1) syms x; f=(3Ax+9Ax)A(1/x);limit(f,x, inf

6、)xans =9(2) syms x y;fb=x*y/(sqrt(x*y+1)-1);limit(limit(fb,x,0),y,0) ans =(3)symsy;fc=(1-cos(xA2+yA2)/(xA2+yA2)*exp(xA2+yA2);limit(limit(fc,x,0),y,0) ans =028.已知参数方程x cost，试求出dy和V|t /3y cost tsintdx dx解 syms t;x=log(cos(t);y=cos(t)_t*si n(t);diff(y,t)/diff(x,t) ans =-(-2*si n( t)-t*cos(t)/si n( t)*c

7、os(t) f=diff(y,t,2)/diff(x,t,2);subs(f,t,sym(pi)/3) ans =3/8-1/24*pi*3A(1/2)X22 f2 f2 f9 .假设 f (x, y) e t dt，试求f 2 f0y x x y y解： syms t x y;f=in t(exp(-tA2),t,0,x*y);F=simple(x/y*diff(f,x,2)-2*diff(diff(f,x),y)+diff(f,y,2)-2*exp(-xA2*yA2)*(-xA2*yA2+1+xA3*y)10.试求出下面的极限。1(1) nim 厂42 162(2n )2 1 (2) li

8、m n(n解( 1)1n221n2 312n syms k n; symsum(1/(2*k)A2-1),k,1, infans =1/2(2) syms k n;limit(n*symsum(1/(nA2+k*pi),k,1,n),n,inf ans =111试求出以下的曲线积分(1)i(xy )dsl为曲线xa(costtsi nt) ya(sin t t cost)(0 t2 )7 0(2)Jyx3ey )dx3y(xy xe2y)dy其中l为a2 2 ,22 2x b y c正向上半椭圆。解( 1)symsa,t;Symsapositive;x=a*(cos(t)+t*si n( t)

9、;y=a*(si n( t)-t*cos(t); f=xA2+yA2;h=i nt(f*sqrt(diff(x,t)A2+diff(y,t)A2),t,0,2*pi)2*aA3*piA2+4*aA3*piA4(2) syms a b c positive;syms t;x=(c/a)*cos(t);y=(c/a)*si n( t);F=y*xA3+exp(y),x*yA3+x*exp(y)-2*y;ds=diff(x,t);diff(y,t); I=i nt(F*ds,t,0,pi)-2/15*c*(-2*cA4+15*aA4)/aA54 a3 a2 aa1b4b3b2b1Ac43 c2 cc

10、1d4d3d2d143212试求出Vandermonde矩阵eeee1 的行列式，并以最简的形式显示 结果。 syms a b c d e;A=aA4,aA3,aA2,a,1;bA4,bA3,bA2,b,1;cA4,cA3,cA2,c,1;dA4,dA3,dA2,d,1;eA 4,eA3,eA2,e,1;simplify(det(A)ans =(a - b)*(a - c)*(a-d)*(b- c)*(a- e)*(b - d)*(b - e)*(c - d)*(c - e)*(d- e)20.50.50.5A01.50.50.5r20.54.50.513 试对矩阵2122 进行 Jordan

11、 变换，并得出变换矩阵。解 A=-2 ;0 ;2 ;2 1 -2 -2;V,J=jordan(A)-4 0 0 00 -2 1 00 0 -2 10 0 0 -214. 试用数值方法和解析方法求取下面的 Sylvester 方程，并验证得出的结果。364052111422432141263673XX2925611310011021964404034663解 A=3 -6 -4 0 5;1 4 2 -2 4;-6 3 -6 7 3;-13 10 0 -11 0;0 4 0 3 4;B=3 -2 1;-2 -9 2;-2 -1 9;C=-2 1 -1;4 1 2;5 -6 1;6 -4 -4;-6

12、 6 -3;X=lyap(A,B,C),norm(A*X+X*B+C)ans =At At 2 At15.假设已知矩阵A如下，试求出e , si nAt , e sin (A e t)解 syms t;A=,0,;,-4,;,1,;0,-1,-1,-3;B=simple(expm(A*t)C=simple(sin(A*t)D=simple(expm(A*t)*si n( AA2*expm(A*t)*t)B =1/2/exp(t)A3-1/2*t/exp(t)A3+1/2/exp(t)A5+1/2*tA2/exp(t)A3,1/2/exp(t)A5-1/2/exp(t)A3+t/exp(t)A3

13、,1/2*t/exp(t)A3+1/2*tA2/exp(t)A3,1/2/exp(t)A5-1/2/exp(t)A3-1/2*t/exp(t)A3+1/2*tA2/exp(t)A31/2*t/exp(t)A3+1/2/exp(t)A5-1/2/exp(t)A3,1/2/exp(t)A3+1/2/exp(t)A5,1/2*t/exp(t)A3,1/2*t/exp(t)A3+1/2/exp(t)A5-1/2/exp(t)A31/2*t/exp(t)A3-1/2/exp(t)A5+1/2/exp(t)A3,-1/2/exp(t)A5+1/2/exp(t)A3,1/exp(t)A3+1/2*t/exp

14、(t)A3,1/2*t/exp(t)A3-1/2/exp(t)A5+1/2/exp(t)A3-1/2*tA2/exp(t)A3,-t/exp(t)A3,-1/2*tA2/exp(t)A3-t/exp(t)A3,1/exp(t)A3-1/2*tA2/exp(t)A3 -sin(9/2*t),0, sin(1/2*t), -sin(3/2*t) -sin(1/2*t),-sin(4*t), sin(1/2*t), -sin(1/2*t) sin(3/2*t),sin(t), -sin(5/2*t), sin(3/2*t) 0, -sin(t), -sin(t), -sin(3*t)(1/2*exp

15、(-3*t)-1/2*t*exp(-3*t)+1/2*exp(-5*t)+1/2*tA2*exp(-3*t)*si n(t*(17/2*e xp(-3*t)-21/2*t*exp(-3*t)+25/2*exp(-5*t)+9/2*tA2*exp(-3*t)+(1/2*exp(-5*t)-1/2 *exp(-3*t)+t*exp(-3*t)*sin(t*(-15/2*exp(-3*t)+9/2*t*exp(-3*t)+25/2*exp(-5*t) +(1/2*t*exp(-3*t)+1/2*tA2*exp(-3*t)*si n(t*(3/2*exp(-3*t)+9/2*t*exp(-3*t)-2

16、5/2* exp(-5*t)+(1/2*exp(-5*t)-1/2*exp(-3*t)-1/2*t*exp(-3*t)+1/2*tA2*exp(-3*t)*s in (t*(-exp(-3*t)+6*t*exp(-3*t)-9/2*tA2*exp(-3*t),(1/2*exp(-3*t)-1/2*t*exp(-3*t)+1/2*exp(-5*t)+1/2*tA2*exp(-3*t)*sin(t*(25/2*exp (-5*t)-21/2*exp(-3*t)+9*t*exp(-3*t)+(1/2*exp(-5*t)-1/2*exp(-3*t)+t*exp(-3*t) *sin(t*(25/2*e

17、xp(-5*t)+9/2*exp(-3*t)+(1/2*t*exp(-3*t)+1/2*tA2*exp(-3*t)*sin( t*(-25/2*exp(-5*t)+9/2*exp(-3*t)+(1/2*exp(-5*t)-1/2*exp(-3*t)-1/2*t*exp(-3*t) +1/2*tA2*exp(-3*t)*sin(t*(6*exp(-3*t)-9*t*exp(-3*t), (1/2*exp(-3*t)-1/2*t*exp(-3*t)+1/2*exp(-5*t)+1/2*tA2*exp(-3*t)*sin(t*(-3/2*t*e xp(-3*t)+9/2*tA2*exp(-3*t)-

18、2*exp(-3*t)+(1/2*exp(-5*t)-1/2*exp(-3*t)+t*exp(-3* t)*sin(t*(9/2*t*exp(-3*t)-3*exp(-3*t)+(1/2*t*exp(-3*t)+1/2*tA2*exp(-3*t)*si n(t*(9/2*t*exp(-3*t)+6*exp(-3*t)+(1/2*exp(-5*t)-1/2*exp(-3*t)-1/2*t*exp(-3*t) +1/2*tA2*exp(-3*t)*sin(t*(-3*t*exp(-3*t)-9/2*tA2*exp(-3*t)+5*exp(-3*t),(1/2*exp(-3*t)-1/2*t*exp

19、(-3*t)+1/2*exp(-5*t)+1/2*tA2*exp(-3*t)*sin(t*(25/2*exp (-5*t)-1/2*exp(-3*t)-21/2*t*exp(-3*t)+9/2*tA2*exp(-3*t)+(1/2*exp(-5*t)-1/2*ex p(-3*t)+t*exp(-3*t)*sin(t*(-15/2*exp(-3*t)+9/2*t*exp(-3*t)+25/2*exp(-5*t)+(1 /2*t*exp(-3*t)+1/2*tA2*exp(-3*t)*sin(t*(3/2*exp(-3*t)+9/2*t*exp(-3*t)-25/2*exp (-5*t)+(1/2

20、*exp(-5*t)-1/2*exp(-3*t)-1/2*t*exp(-3*t)+1/2*tA2*exp(-3*t)*sin(t* (8*exp(-3*t)+6*t*exp(-3*t)-9/2*tA2*exp(-3*t)(1/2*t*exp(-3*t)+1/2*exp(-5*t)-1/2*exp(-3*t)*sin(t*(17/2*exp(-3*t)-21/2*t*exp(-3*t)+25/ 2*exp(-5*t)+9/2*tA2*exp(-3*t)+(1/2*exp(-3*t)+1/2*exp(-5*t)*si n(t*(-15/2*exp(-3*t)+9/2*t*exp(-3*t)+25/

21、2*exp(-5*t)+1/2*t*exp(-3*t)*sin(t*(3/2*exp(-3*t)+9/2 *t*exp(-3*t)-25/2*exp(-5*t)+(1/2*t*exp(-3*t)+1/2*exp(-5*t)-1/2*exp(-3*t)*sin (t*(-exp(-3*t)+6*t*exp(-3*t)-9/2*tA2*exp(-3*t),(1/2*t*exp(-3*t)+1/2*exp(-5*t)-1/2*exp(-3*t)*sin(t*(25/2*exp(-5*t)-21/2*exp(-3 *t)+9*t*exp(-3*t)+(1/2*exp(-3*t)+1/2*exp(-5*

22、t)*sin(t*(25/2*exp(-5*t)+9/2*exp (-3*t)+1/2*t*exp(-3*t)*sin(t*(-25/2*exp(-5*t)+9/2*exp(-3*t)+(1/2*t*exp(-3*t )+1/2*exp(-5*t)-1/2*exp(-3*t)*sin(t*(6*exp(-3*t)-9*t*exp(-3*t),(1/2*t*exp(-3*t)+1/2*exp(-5*t)-1/2*exp(-3*t)*sin(t*(-3/2*t*exp(-3*t)+9/2*tA2*e xp(-3*t)-2*exp(-3*t)+(1/2*exp(-3*t)+1/2*exp(-5*t)

23、*sin(t*(9/2*t*exp(-3*t)-3*e xp(-3*t)+1/2*t*exp(-3*t)*sin(t*(9/2*t*exp(-3*t)+6*exp(-3*t)+(1/2*t*exp(-3*t )+1/2*exp(-5*t)-1/2*exp(-3*t)*sin(t*(-3*t*exp(-3*t)-9/2*tA2*exp(-3*t)+5*exp(-3 *t),(1/2*t*exp(-3*t)+1/2*exp(-5*t)-1/2*exp(-3*t)*sin(t*(25/2*exp(-5*t)-1/2*exp(-3* t)-21/2*t*exp(-3*t)+9/2*tA2*exp(-3

24、*t)+(1/2*exp(-3*t)+1/2*exp(-5*t)*sin(t*(-1 5/2*exp(-3*t)+9/2*t*exp(-3*t)+25/2*exp(-5*t)+1/2*t*exp(-3*t)*sin(t*(3/2*exp(- 3*t)+9/2*t*exp(-3*t)-25/2*exp(-5*t)+(1/2*t*exp(-3*t)+1/2*exp(-5*t)-1/2*exp(-3 *t)*sin(t*(8*exp(-3*t)+6*t*exp(-3*t)-9/2*tA2*exp(-3*t)(1/2*t*exp(-3*t)-1/2*exp(-5*t)+1/2*exp(-3*t)*si

25、n(t*(17/2*exp(-3*t)-21/2*t*exp(-3*t)+25/2*exp(-5*t)+9 /2*tA2*exp(-3*t)+(-1/2*exp(-5*t)+1/2*exp(-3*t)*sin(t*(-15/2*exp(-3*t)+9/2*t* exp(-3*t)+25/2*exp(-5*t)+(exp(-3*t)+1/2*t*exp(-3*t)*sin(t*(3/2*exp(-3*t)+9/2 *t*exp(-3*t)-25/2*exp(-5*t)+(1/2*t*exp(-3*t)-1/2*exp(-5*t)+1/2*exp(-3*t)*sin (t*(-exp(-3*t)+

26、6*t*exp(-3*t)-9/2*tA2*exp(-3*t),(1/2*t*exp(-3*t)-1/2*exp(-5*t)+1/2*exp(-3*t)*sin(t*(25/2*exp(-5*t)-21/2*exp(-3 *t)+9*t*exp(-3*t)+(-1/2*exp(-5*t)+1/2*exp(-3*t)*sin(t*(25/2*exp(-5*t)+9/2*ex p(-3*t)+(exp(-3*t)+1/2*t*exp(-3*t)*sin(t*(-25/2*exp(-5*t)+9/2*exp(-3*t)+(1/2*t*exp(-3*t)-1/2*exp(-5*t)+1/2*exp(-

27、3*t)*sin(t*(6*exp(-3*t)-9*t*exp(-3*t), (1/2*t*exp(-3*t)-1/2*exp(-5*t)+1/2*exp(-3*t)*sin(t*(-3/2*t*exp(-3*t)+9/2*tA2*e xp(-3*t)-2*exp(-3*t)+(-1/2*exp(-5*t)+1/2*exp(-3*t)*sin(t*(9/2*t*exp(-3*t)-3* exp(-3*t)+(exp(-3*t)+1/2*t*exp(-3*t)*sin(t*(9/2*t*exp(-3*t)+6*exp(-3*t)+(1 /2*t*exp(-3*t)-1/2*exp(-5*t)+1

28、/2*exp(-3*t)*sin(t*(-3*t*exp(-3*t)-9/2*tA2*exp(-3*t)+5*exp(-3*t), (1/2*t*exp(-3*t)-1/2*exp(-5*t)+1/2*exp(-3*t)*sin(t*(25/2*exp(-5*t)-1/2*exp(-3* t)-21/2*t*exp(-3*t)+9/2*tA2*exp(-3*t)+(-1/2*exp(-5*t)+1/2*exp(-3*t)*sin(t*(- 15/2*exp(-3*t)+9/2*t*exp(-3*t)+25/2*exp(-5*t)+(exp(-3*t)+1/2*t*exp(-3*t)*sin (

29、t*(3/2*exp(-3*t)+9/2*t*exp(-3*t)-25/2*exp(-5*t)+(1/2*t*exp(-3*t)-1/2*exp(-5* t)+1/2*exp(-3*t)*sin(t*(8*exp(-3*t)+6*t*exp(-3*t)-9/2*tA2*exp(-3*t)-1/2*tA2*exp(-3*t)*sin(t*(17/2*exp(-3*t)-21/2*t*exp(-3*t)+25/2*exp(-5*t)+9/2*tA 2*exp(-3*t)-t*exp(-3*t)*sin(t*(-15/2*exp(-3*t)+9/2*t*exp(-3*t)+25/2*exp(-5*t

30、) )+(-1/2*tA2*exp(-3*t)-t*exp(-3*t)*sin(t*(3/2*exp(-3*t)+9/2*t*exp(-3*t)-25/2*e xp(-5*t)+(exp(-3*t)-1/2*tA2*exp(-3*t)*si n(t*(-exp(-3*t)+6*t*exp(-3*t)-9/2*tA 2*exp(-3*t),-1/2*tA2*exp(-3*t)*si n(t*(25/2*exp(-5*t)-21/2*exp(-3*t)+9*t*exp(-3*t)-t*exp(- 3*t)*si n( t*(25/2*exp(-5*t)+9/2*exp(-3*t)+(-1/2*tA

31、2*exp(-3*t)-t*exp(-3*t)*s in (t*(-25/2*exp(-5*t)+9/2*exp(-3*t)+(exp(-3*t)-1/2*tA2*exp(-3*t)*si n( t*(6*exp( -3*t)-9*t*exp(-3*t),-1/2*tA2*exp(-3*t)*s in (t*(-3/2*t*exp(-3*t)+9/2*tA2*exp(-3*t)-2*exp(-3*t)-t*ex p(-3*t)*si n(t*(9/2*t*exp(-3*t)-3*exp(-3*t)+(-1/2*tA2*exp(-3*t)-t*exp(-3*t)*s in (t*(9/2*t*e

32、xp(-3*t)+6*exp(-3*t)+(exp(-3*t)-1/2*tA2*exp(-3*t)*si n(t*(-3*t*e xp(-3*t)-9/2*tA2*exp(-3*t)+5*exp(-3*t),-1/2*tA2*exp(-3*t)*si n(t*(25/2*exp(-5*t)-1/2*exp(-3*t)-21/2*t*exp(-3*t)+9/2*tA2 *exp(-3*t)-t*exp(-3*t)*si n(t*(-15/2*exp(-3*t)+9/2*t*exp(-3*t)+25/2*exp(-5*t) )+(-1/2*tA2*exp(-3*t)-t*exp(-3*t)*si

33、n(t*(3/2*exp(-3*t)+9/2*t*exp(-3*t)-25/2*ex p(-5*t)+(exp(-3*t)-1/2*tA2*exp(-3*t)*si n(t*(8*exp(-3*t)+6*t*exp(-3*t)-9/2*tA 2*exp(-3*t)第二部分1.对下列的函数f (t)进行Lap lace变换。(1) fa (t)； (2) fb(t) t5sin t ； (3)fc(t) t8cos t解：(1) syms t alpha;f=sin(alpha*t)/t;F=laplace(f)F =ata n( alpha/s)(2) syms t alpha;f=tA5*s

34、in(alpha*t);F=laplace(f)F =120/(sA2+alphaA2)A3*si n( 6*ata n(alpha/s)(3) syms t alpha;f=tA8*cos(alpha*t);F=laplace(f)F =40320/(sA2+alphaA2F(9/2)*cos(9*ata n(alpha )2.对下面的F(s)式进行Laplace反变换。(1)Fa(S)s2(s2 a2)(s b)；2) Fb (s)vs a vs b (3)Fc(s)ln-(1) syms s a b;f=1/(sqrt(sA2)*(sA2-aA2)*(s+b);F=ilaplace(f)

35、F =-1/2/(a-b)/aA2*exp(-a*t)+1/2/(a+b)/aA2*exp(a*t)-1/aA2/b+1/b/(aA2-bA2)*exp(-b*t)(2) syms s a b;f=sqrt(s_a)_sqrt(s_b);F=ilaplace(f)F =1/2/t/(t*pi)A(1/2)*(exp(b*t)-exp(a*t)(3) syms s a b; f=log(s-a)/(s-b);F=ilaplace(f)F =(exp(b*t)-exp(a*t)/t3.试求出下面函数的Fourier变换，对得出的结果再进行Fourier反变换，观察 是否能得出原来函数。(1)f(x

36、) x2(32x),0 x 2 ；(2)f(t) t2(t 2 )2,0t 2 。解(1) syms x;f=xA2*(3*pi-2*abs(x);F=fourier(f)f仁ifourier(F)F =-6*(4+piA2*dirac(2,w)*wA4)/wA4 fl =xA2*(-4*x*heaviside(x)+3*pi+2*x) (2) syms t; f=tA2*(t-2*pi)A2; F=fourier(f) f1=ifourier(F)2*pi*(-4*piA2*dirac(2,w)+4*i*pi*dirac(3,w)+dirac(4,w)fl = xA2*(2*pi-x)A24

37、.请将下述时域序列函数f(kT)进行Z变换，并对结果进行反变换检验。(1 )fa(kT) cos(kaT) ；( 2) fb(kT) (kT)2e akT ；( 3)1fc(kT)-(akT 1 e akT )。a解(1)syms a T k z;f=cos(k*a*T);F=ztra ns(f,k,z)f1=iztra ns(F, z,k)(z-cos(a*T)*z/(zA2-2*z*cos(a*T)+1)f1 =cos(k*a*T)(2)syms a T k z;f=(k*T)A2*exp(-a*k*T);F=ztrans(f,k,z) f1=iztrans(F,z,k)F =TA2*z*

38、exp(-a*T)*(z+exp(-a*T)/(z-exp(-a*T)A3 f1 =TA2*(1/exp(a*T)Ak*kA2(3)syms a T k z;f=(1/a)*(a*k*T-1+exp(-a*k*T);F=ztrans(f,k,z)f1=iztrans(F,z,k)F =1/a*(a*T*z/(z-1)A2-z/(z-1)+z/exp(-a*T)/(z/exp(-a*T)-1) f1 = (k*a*T+(1/exp(a*T)Ak-1)/a5. 用数值求解函数求解下述一元和二元方程的根，并对得出的结果进行检验。(1) f (x) e (x 1) 解/2sin(5x 2)；(2) f

39、(x,y) (x2xy)ex2y 2 xy(1)syms x;f=exp(-(x+1)A2+pi/2)*sin(5*x+2);t=solve(f)subs(f,x,-2/5)t =-2/5ans =0(2) syms x y; f=(xA2+yA2+x*y)*exp(-xA2-yA2-x*y);x1=solve(xA2+yA2+x*y)*exp(-xA2-yA2-x*y),x)simple(subs(f,x,x1)x1 =(-1/2+1/2*i*3A(1/2)*y(-1/2-1/2*i*3A(1/2)*yans =0016. 试求出使得 (ex cx) 2 dx 取得极小值的 c 值 0解 s

40、yms c x;f=(exp(x)-c*x)A2;F=int(f,x,0,1);f1=diff(F,c);solve(f1) ans =37. 试求解下面的非线性规划问题。min ex1 (4x12 2x22 4x1x2 2x21)x1 x20x1x2x1x2 1.5x s.t.x1x21010x1,x2 10解可以用下面的语句描述目标函数：function y=exc6fun6(x)y=exp(x(1)*(4*x(1)A2+2*x(2)A2+4*x(1)*x (2)+2*x (2)+1);这时调用非线性最优化问题求解函数可以得出如下结果： A=; B=; Aeq=; Beq=; xm=-10

41、; -10; xM=10; 10;x0=(xm+xM)/2;ff=optimset;=1e-10;=1e-20;x=fmincon( exc6fun6 ,x0,A,B,Aeq,Beq,xm,xM, exc6fun6a ,ff)Maximum number of function evaluations exceeded;increasex =可以看出该结果并非原问题的解，故继续求解如下： i=1; x=x0;while (1)x,a,b=fmincon(exc6fun6 ,x,A,B,Aeq,Beq,xm,xM, exc6fun6a ,ff);if b0, break; endi=i+1;en

42、dx,ix =i =8.求解下面的整数线性规划问题。max (592x1381x2273x355x448x537x623x7)x 0x s.t3534x1 2356x2 1767x3 589x4 528x5 451x6 304x7 119567 f=-592 381 273 55 48 37 23;A=3534 2356 1767 589 528 451 304; B=119567;intlist=1;1;1;1;1;1;1;ctype=-1; xm=zeros(7,1); xM=i nf*o nes(7,1);res,b=ipslv_mex(f,A,B,i ntlist,xM,xm,ctyp

43、e)res =3221000009.试求出微分方程y(x) (2)y(x) (1丄)y(x)x2e 5x的解析解通解，并求出xx满足边界条件y(1),y( )1的解析解。解 syms x y;y1=dsolve(D2y-(2-1/x)*Dy+(1-1/x)*y=xA2*exp(-5*x),x) y1 = exp(x)*C2+exp(x)*log(x)*C1+1/1296*(6*exp(6*x)*Ei(1,6*x)+11+30*x+36*xA2)*exp(-5*x) y=dsolve(D2y-(2-1/x)*Dy+(1-1/x)*y=xA2*exp(-5*x),y(1)=sym(pi),y(sy

44、m(pi)=1,x)y =-1/1296*exp(x)*(6*exp(1)*Ei(1,6)+77*exp(-5)-1296*sym(pi)/exp(1)-1/1296*exp(x)* log(x)*(-6*Ei(1,6)*exp(6*sym(pi)+6)-77*exp(6*sym(pi)+1296*sym(pi)*exp(6*sym(pi )+5)-3*i*pi*csgn(sym(pi)*exp(6*sym(pi)+6)+6*Ei(1,6*sym(pi)*exp(6*sym(pi)+6)+3 *i*pi*exp(6*sym(pi)+6)+3*i*pi*csgn(6*i*sym(pi)*exp(6*sym(pi)+6)+30*sym(pi)*exp (6)-3*i*pi*csgn(sym(pi)*csgn(6*i*sym(pi)*exp(6*sym(pi)+6)+36*sym(pi)A2*exp(6) +11*exp(6)-1296*exp(5*sym(pi)+6)/log(sym(pi)*exp(-6*sym(pi)-6)+1/1296*(6