What is the solution for y^{''}-4y=10e^{-2x} ?

The solution for y^{''}-4y=10e^{-2x} is y=c_{1}e^{2x}+c_{2}e^{-2x}-(5e^{-2x}x)/2

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y^{''}-4y=10e^{-2x}

y^{^{''}} - 4 y = 10 e^{- 2 x}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{5 e ^{- 2 x} x}{2}

Solution steps

y^{''} (x) - 4 y = 10 e^{- 2 x}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{5 e ^{- 2 x} x}{2}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} - \frac{5 e ^{- 2 x} x}{2}

y^{^{''}} + 2 y^{^{'}} + 10 y = x, y (0) = 0, y^{^{'}} (0) = - 1

y^{^{''}} + 17 y = e^{6 x}

y^{^{''}} - y = sin (t), y (0) = 1, y (0) = - 1

y^{^{''}} + y = 6 e^{- 2 x}, y (0) = 0, y^{^{'}} (0) = 0

y^{^{''}} - y^{^{'}} - 2 y = x^{2} sin (2 x)

What is the solution for y^{''}-4y=10e^{-2x} ?
The solution for y^{''}-4y=10e^{-2x} is y=c_{1}e^{2x}+c_{2}e^{-2x}-(5e^{-2x}x)/2