What is the solution for y^'=2y+x^2e^{2x} ?

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

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y^'=2y+x^2e^{2x}

y^{^{'}} = 2 y + x^{2} e^{2 x}

y = \frac{x ^{3}}{3 e ^{- 2 x}} + c_{1} e^{2 x}

Solution steps

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

Solve linear ODE:

y = \frac{x ^{3}}{3 e ^{- 2 x}} + c_{1} e^{2 x}

y = \frac{x ^{3}}{3 e ^{- 2 x}} + c_{1} e^{2 x}

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

\frac{4 x}{x + 3}

y = \frac{2}{x}

\frac{\partial}{\partial x} (3 x^{4} e^{x^{2} y})

x \to - 3 + lim (\frac{3}{x ^{2} - 9})

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