matlab求解微分方程的通解问题解某微分方程：x^2*D2y+x*Dy+(x^2-1/2)*y=0,初值：y(pi/2)=2,Dy(pi/2)=-2/pi,书本标准答案为：ans=2^(1/2)*pi*^(1/2)/x^(1/2)*sin(x)；但我运行：dsolve(#39;x^2*D2y+x*Dy+(x^2-1/2)*y=0#39;,#39;y(pi/2)=2,Dy(p

问题：matlab求解微分方程的通解问题解某微分方程：x^2*D2y+x*Dy+(x^2-1/2)*y=0,初值：y(pi/2)=2,Dy(pi/2)=-2/pi,书本标准答案为：ans=2^(1/2)*pi*^(1/2)/x^(1/2)*sin(x)；但我运行：dsolve(#39;x^2*D2y+x*Dy+(x^2-1/2)*y=0#39;,#39;y(pi/2)=2,Dy(p

答案：↓↓↓

韩永的回答：

网友采纳　　symsxy　　y=sqrt(2*pi/x)*sin(x);y1=diff(y,'x');y2=diff(y,'x',2);　　h=x^2*y2+x*y1+(x^2-1/2)*y;h=simplify(h)　　结果：　　h=　　-1/4/x*2^(1/2)*sin(x)*pi^(1/2)/(1/x)^(1/2)　　可见不等于0,=y,说明原答案有问题