What is the solution for y^{''}-16y=7e^{4x} ?

The solution for y^{''}-16y=7e^{4x} is y=c_{1}e^{4x}+c_{2}e^{-4x}+(7e^{4x}x)/8

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y^{''}-16y=7e^{4x}

y^{^{''}} - 16 y = 7 e^{4 x}

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} + \frac{7 e ^{4 x} x}{8}

Solution steps

y^{''} (x) - 16 y = 7 e^{4 x}

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} + \frac{7 e ^{4 x} x}{8}

y = c_{1} e^{4 x} + c_{2} e^{- 4 x} + \frac{7 e ^{4 x} x}{8}

y^{^{'''}} - y^{^{''}} = t

y^{^{''}} - 10 y^{^{'}} + 25 y = x cos (5 x)

y^{^{''}} + 9 y = 3 x, y (0) = 1, y^{^{'}} (0) = 3

y^{^{'''}} + 8 y^{^{''}} - 13 y^{^{'}} - 140 y = 4 e^{4} t

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

What is the solution for y^{''}-16y=7e^{4x} ?
The solution for y^{''}-16y=7e^{4x} is y=c_{1}e^{4x}+c_{2}e^{-4x}+(7e^{4x}x)/8