matlab求解微分方程的通解問題
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,書本標(biāo)準(zhǔn)答案為：
ans=2^(1/2)*pi*^(1/2)/x^(1/2)*sin(x)；
但我運(yùn)行：dsolve('x^2*D2y+x*Dy+(x^2-1/2)*y=0','y(pi/2)=2,Dy(pi/2)=-2/pi','x')
ans =
(2*bessely(-2^(1/2)/2,x)*(2^(1/2)*besselj(-2^(1/2)/2,pi/2) - besselj(-2^(1/2)/2,pi/2) + pi*besselj(1 - 2^(1/2)/2,pi/2)))/(pi*(besselj(1 - 2^(1/2)/2,pi/2)*bessely(-2^(1/2)/2,pi/2) - bessely(1 - 2^(1/2)/2,pi/2)*besselj(-2^(1/2)/2,pi/2))) - (2*besselj(-2^(1/2)/2,x)*(2^(1/2)*bessely(-2^(1/2)/2,pi/2) - bessely(-2^(1/2)/2,pi/2) + pi*bessely(1 - 2^(1/2)/2,pi/2)))/(pi*(besselj(1 - 2^(1/2)/2,pi/2)*bessely(-2^(1/2)/2,pi/2) - bessely(1 - 2^(1/2)/2,pi/2)*besselj(-2^(1/2)/2,pi/2)))
即使我simpify(ans),j結(jié)果還是一樣,怎么回事啊?