Question

求解微分方程 y'-y/x=(x^2)y

Answer 1

y'-y/x=(x^2)y 即 dy/dx =y/x+(x^2)y =y(1/x + x^2)
分离变量,得 1/y dy = (1/x + x^2) dx
两边积分,得 ∫1/y dy = ∫(1/x + x^2) dx
即ln|y| = ln|x| + 1/3 x^3 + C1
化简,得 y = C x e^(1/3 x^3)