What is the solution for 4y^{''}-y=12+6x ?

The solution for 4y^{''}-y=12+6x is y=c_{1}e^{x/2}+c_{2}e^{-x/2}-6x-12

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4y^{''}-y=12+6x

4 y^{^{''}} - y = 12 + 6 x

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- \frac{x}{2}} - 6 x - 12

Solution steps

4 y^{''} (x) - y = 12 + 6 x

Solve linear ODE:

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- \frac{x}{2}} - 6 x - 12

y = c_{1} e^{\frac{x}{2}} + c_{2} e^{- \frac{x}{2}} - 6 x - 12

y^{^{''}} - 3 y^{^{'}} - 4 y = 3 e^{2 t}

y^{^{''}} - 2 y^{^{'}} + 3 y = e^{x}

y^{^{''}} - 3 y^{^{'}} = 8 e^{2 t} - 2 e^{- t}

y^{^{''}} - 2 y^{^{'}} + y = t

y^{^{''}} - 4 y^{^{'}} = 8 e^{6 x} (x - 1)

What is the solution for 4y^{''}-y=12+6x ?
The solution for 4y^{''}-y=12+6x is y=c_{1}e^{x/2}+c_{2}e^{-x/2}-6x-12