What is the solution for (dy)/(dx)-2y=x^2e^{2x} ?

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

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(dy)/(dx)-2y=x^2e^{2x}

\frac{d y}{d x} - 2 y = x^{2} e^{2 x}

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

Solution steps

\frac{d y}{d 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}

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