What is the solution for y^{''}-25y=e^{5x} ?

The solution for y^{''}-25y=e^{5x} is y=c_{1}e^{5x}+c_{2}e^{-5x}+(e^{5x}x)/(10)

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y^{''}-25y=e^{5x}

y^{^{''}} - 25 y = e^{5 x}

y = c_{1} e^{5 x} + c_{2} e^{- 5 x} + \frac{e ^{5 x} x}{10}

Solution steps

y^{''} (x) - 25 y = e^{5 x}

Solve linear ODE:

y = c_{1} e^{5 x} + c_{2} e^{- 5 x} + \frac{e ^{5 x} x}{10}

y = c_{1} e^{5 x} + c_{2} e^{- 5 x} + \frac{e ^{5 x} x}{10}

y^{^{''}} + 2 y = cos (8 t)

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

y^{^{''}} + 4 y = t^{2} + 3 e t, y (0) = 0, y^{^{'}} (0) = 2

y^{^{''}} - y^{^{'}} - y = x^{3}

y^{^{''}} + 9 y = sin (x) + cos (x)

What is the solution for y^{''}-25y=e^{5x} ?
The solution for y^{''}-25y=e^{5x} is y=c_{1}e^{5x}+c_{2}e^{-5x}+(e^{5x}x)/(10)