求微分方程的通解：x^2(d^2y/dx^2)=(dy/dx)^2+2x(dy/dx)高阶微分方程求解.....

求微分方程的通解：x^2(d^2y/dx^2)=(dy/dx)^2+2x(dy/dx)高阶微分方程求解.....
求微分方程的通解：x^2(d^2y/dx^2)=(dy/dx)^2+2x(dy/dx)
高阶微分方程求解.....

求微分方程的通解：x^2(d^2y/dx^2)=(dy/dx)^2+2x(dy/dx)高阶微分方程求解.....
x^2y''-2xy'=y'^2
-(2xy'-x^2y'')/y'^2=1
(x^2/y')'=-1
两边积分：x^2/y'=-x+C1
y'=x^2/(-x+C1)=(x^2-C1x+C1x-C1^2+C1^2)/(-x+C1)=-x-C1+C1^2/(-x+C1)
两边积分：y=-x^2/2-C1x-C1^2ln|-x+C1|+C2