求微分方程xy''=(1+2x^2)y'的通解是,
问题描述：
求微分方程xy''=(1+2x^2)y'的通解是,
答
xy''=y'+2x^2y'xy''-y'=2x^2y' 两边同除以x^2(xy''-y')/x^2=2y'(y'/x)=2y+cy'/(2y+c)=x1/2 ln(2y+c1)=1/2 x^2+c2ln(2y+C1)=x^2+C22y+C1=e^(x^2+C2) =C2* e^(x^2)y= C1 * e^(x^2)+C2