What is the solution for (d^2y)/(dx^2)-y=2e^x+6e^{2x} ?

The solution for (d^2y)/(dx^2)-y=2e^x+6e^{2x} is y=c_{1}e^x+c_{2}e^{-x}+e^xx+2e^{2x}

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(d^2y)/(dx^2)-y=2e^x+6e^{2x}

\frac{d ^{2} y}{d x ^{2}} - y = 2 e^{x} + 6 e^{2 x}

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

Solution steps

\frac{d ^{2} y}{d x ^{2}} - y = 2 e^{x} + 6 e^{2 x}

Solve linear ODE:

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

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

\frac{\partial}{\partial x} (2 x cos (x) cos (y))

\int_{0}^{4} x + 2 d x

\frac{d ^{2}}{d x ^{2}} (e^{4 x})

\frac{d}{d x} ((3 x^{2} - 4 x) e^{5 x})

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

What is the solution for (d^2y)/(dx^2)-y=2e^x+6e^{2x} ?
The solution for (d^2y)/(dx^2)-y=2e^x+6e^{2x} is y=c_{1}e^x+c_{2}e^{-x}+e^xx+2e^{2x}