What is the solution for y^{'''}+2y^{''}=12x+4 ?

The solution for y^{'''}+2y^{''}=12x+4 is y=c_{1}e^{-2x}+c_{2}+c_{3}x+x^3-(x^2)/2

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y^{'''}+2y^{''}=12x+4

y^{^{'''}} + 2 y^{^{''}} = 12 x + 4

y = c_{1} e^{- 2 x} + c_{2} + c_{3} x + x^{3} - \frac{x ^{2}}{2}

Solution steps

y^{'''} (x) + 2 y^{''} (x) = 12 x + 4

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} + c_{3} x + x^{3} - \frac{x ^{2}}{2}

y = c_{1} e^{- 2 x} + c_{2} + c_{3} x + x^{3} - \frac{x ^{2}}{2}

y^{^{''}} + 25 y = 25 sec^{2} (5 t)

x^{''} + 2 x = 8, x (π) = 0, x (0) = 0

y^{^{''}} - y^{^{'}} - 42 y = - 122 t + 84 t^{2}

\frac{d ^{2} y}{d t ^{2}} + 12 \frac{d y}{d t} + 36 y = - 4 t + 3

y^{^{''}} - 2 y^{^{'}} = 4 x + e^{x}

What is the solution for y^{'''}+2y^{''}=12x+4 ?
The solution for y^{'''}+2y^{''}=12x+4 is y=c_{1}e^{-2x}+c_{2}+c_{3}x+x^3-(x^2)/2