differential equation?

xy' - y + 3x³y - x⁴ = 0
xy' + ( 3x³ - 1 )y - x⁴ = 0
y' + ( 3x² - 1/x )y = x³ ..... (1式)
此為一階線性ODE

積分因子 μ
= e^[ ∫ ( 3x² - 1/x ) dx ]
= e^( x³ - ln x )
= e^x³ / e^( ln x )
= (1/x)e^x³

(1式) 乘以積分因子後 :
(1/x)(e^x³)y' + ( 3x - 1/x² )(e^x³)y = x²(e^x³)
d/dx [ (1/x)(e^x³)y ] = x²(e^x³)
(1/x)(e^x³)y = ∫ x²(e^x³) dx = (1/3)e^x³ + c
y = x*e^(-x³)[ (1/3)e^x³ + C ] = x/3 + cx*e^(-x³)

Ans: y = x/3 + cx*e^(-x³)