What is the solution for y^{''}-16y=2e^{4t} ?

The solution for y^{''}-16y=2e^{4t} is y=c_{1}e^{4t}+c_{2}e^{-4t}+(e^{4t}t)/4

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y^{''}-16y=2e^{4t}

y^{^{''}} - 16 y = 2 e^{4 t}

y = c_{1} e^{4 t} + c_{2} e^{- 4 t} + \frac{e ^{4 t} t}{4}

Solution steps

y^{''} (t) - 16 y = 2 e^{4 t}

Solve linear ODE:

y = c_{1} e^{4 t} + c_{2} e^{- 4 t} + \frac{e ^{4 t} t}{4}

y = c_{1} e^{4 t} + c_{2} e^{- 4 t} + \frac{e ^{4 t} t}{4}

y^{^{''}} + 4 y = 3 csc (t)

x^{^{''}} + 2 x^{^{'}} + x = e^{- 2 t}, x (0) = 2, x^{^{'}} (0) = 1

(D - 2)^{2} y = 20 - 3 x e^{2 x}

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

y^{^{''}} + 16 y = sec (4 t)

What is the solution for y^{''}-16y=2e^{4t} ?
The solution for y^{''}-16y=2e^{4t} is y=c_{1}e^{4t}+c_{2}e^{-4t}+(e^{4t}t)/4