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

The solution for (d^2y)/(dx^2)-(dy)/(dx)-2y=e^{3x} is y=c_{1}e^{2x}+c_{2}e^{-x}+1/4 e^{3x}

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(d^2y)/(dx^2)-(dy)/(dx)-2y=e^{3x}

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 2 y = e^{3 x}

y = c_{1} e^{2 x} + c_{2} e^{- x} + \frac{1}{4} e^{3 x}

Solution steps

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 2 y = e^{3 x}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- x} + \frac{1}{4} e^{3 x}

y = c_{1} e^{2 x} + c_{2} e^{- x} + \frac{1}{4} e^{3 x}

y^{^{''}} + 3 y^{^{'}} - 10 y = e^{x} cos (3 x)

y^{^{''}} - 2 y^{^{'}} - 3 y = 4 e^{t}

y^{^{''}} - 4 y^{^{'}} + 8 y = e^{2 x} (sin (2 x) - cos (2 x))

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

y^{^{''}} - 3 y^{^{'}} - 28 y = 528 e^{- t}

What is the solution for (d^2y)/(dx^2)-(dy)/(dx)-2y=e^{3x} ?
The solution for (d^2y)/(dx^2)-(dy)/(dx)-2y=e^{3x} is y=c_{1}e^{2x}+c_{2}e^{-x}+1/4 e^{3x}