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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} - 8 y^{^{'}} + 2 y = t e^{t}

y^{^{''}} - 2 y^{^{'}} + 2 y = cos (2 x)

y^{^{''}} - 5 y^{^{'}} + 6 y = 9 x + 2 e^{x}

y^{^{''}} + 3 y^{^{'}} + 2 y = 26 x + 47

y^{^{''}} + y^{^{'}} = x, y (0) = 8, y^{^{'}} (0) = 0

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