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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

x^{^{''}} + 2 x = 2 t + 26

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

y^{^{''}} - 14 y^{^{'}} + 49 y = e^{7 t} ln (t)

y^{^{''}} + 2 y = \frac{1}{cos ( 2 x )}

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

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