What is the solution for y^{''}-4y=e^{5x} ?

The solution for y^{''}-4y=e^{5x} is y=c_{1}e^{2x}+c_{2}e^{-2x}+1/21 e^{5x}

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y^{''}-4y=e^{5x}

y^{^{''}} - 4 y = e^{5 x}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + \frac{1}{21} e^{5 x}

Solution steps

y^{''} (x) - 4 y = e^{5 x}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + \frac{1}{21} e^{5 x}

y = c_{1} e^{2 x} + c_{2} e^{- 2 x} + \frac{1}{21} e^{5 x}

y^{^{'''}} - 2 y^{^{''}} + y^{^{'}} = 9

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

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

y^{^{''}} + y^{^{'}} - 12 y = x e^{2 x}

x^{^{''}} - 2 x^{^{'}} - x = e^{2 t}

What is the solution for y^{''}-4y=e^{5x} ?
The solution for y^{''}-4y=e^{5x} is y=c_{1}e^{2x}+c_{2}e^{-2x}+1/21 e^{5x}