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}

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\frac{d}{d x} (3 x^{2} - e^{x})

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}