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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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