Question

求微分方程dy/dx=x²-y/x的通解

Answer 1

p(x) =1/x
e^[∫p(x)dx]=x
//
dy/dx=x^2 -y/x
dy/dx + y/x = x^2
两边乘以x
x.[dy/dx + y/x] = x^3
d/dx(xy ) = x^3
xy=∫ x^3 dx
=(1/4)x^4 +C
y=(1/4)x^3 +C/x