What is the solution for xy^'+(1+2x^2)y=x^3e^{-x^2} ?

The solution for xy^'+(1+2x^2)y=x^3e^{-x^2} is y=(x^3)/(4e^{x^2)}+(c_{1})/(e^{x^2)x}

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xy^'+(1+2x^2)y=x^3e^{-x^2}

x y^{^{'}} + (1 + 2 x^{2}) y = x^{3} e^{- x^{2}}

y = \frac{x ^{3}}{4 e ^{x^{2}}} + \frac{c _{1}}{e ^{x^{2}} x}

Solution steps

x y^{'} (x) + (1 + 2 x^{2}) y = x^{3} e^{- x^{2}}

Solve linear ODE:

y = \frac{x ^{3}}{4 e ^{x^{2}}} + \frac{c _{1}}{e ^{x^{2}} x}

y = \frac{x ^{3}}{4 e ^{x^{2}}} + \frac{c _{1}}{e ^{x^{2}} x}

\frac{d}{d x} (sec (7 x))

\frac{d}{d x} (2 x (x + 1)^{2})

x \to 3 + lim (\frac{x}{3 x - x ^{3}})

\frac{d}{d x} ((sin (x))^{2})

x \to 0 lim ((cos (x))^{c o t^{2} (x)})

What is the solution for xy^'+(1+2x^2)y=x^3e^{-x^2} ?
The solution for xy^'+(1+2x^2)y=x^3e^{-x^2} is y=(x^3)/(4e^{x^2)}+(c_{1})/(e^{x^2)x}