What is the solution for y^{''}-2y^'-8y=5e^2x ?

The solution for y^{''}-2y^'-8y=5e^2x is y=c_{1}e^{4x}+c_{2}e^{-2x}-(5e^2x)/8+(5e^2)/(32)

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y^{''}-2y^'-8y=5e^2x

y^{^{''}} - 2 y^{^{'}} - 8 y = 5 e^{2} x

y = c_{1} e^{4 x} + c_{2} e^{- 2 x} - \frac{5 e ^{2} x}{8} + \frac{5 e ^{2}}{32}

Solution steps

y^{''} (x) - 2 y^{'} (x) - 8 y = 5 e^{2} x

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{- 2 x} - \frac{5 e ^{2} x}{8} + \frac{5 e ^{2}}{32}

y = c_{1} e^{4 x} + c_{2} e^{- 2 x} - \frac{5 e ^{2} x}{8} + \frac{5 e ^{2}}{32}

(d^{2} + 1) y = e^{- x} + cos (x) + x^{3}

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

(2 d^{2} - d - 3) y = 25 e^{- x}

(d^{2} - 4 d + 4) \cdot y = 8 x^{2} + e^{2 x}

y^{^{'''}} + 6 y^{^{''}} = x^{2}

What is the solution for y^{''}-2y^'-8y=5e^2x ?
The solution for y^{''}-2y^'-8y=5e^2x is y=c_{1}e^{4x}+c_{2}e^{-2x}-(5e^2x)/8+(5e^2)/(32)