What is the solution for y^{'''}+2y^{''}=32e^{2x}+24x ?

The solution for y^{'''}+2y^{''}=32e^{2x}+24x is y=c_{1}e^{-2x}+c_{2}+c_{3}x+2e^{2x}+2x^3-3x^2

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y^{'''}+2y^{''}=32e^{2x}+24x

y^{^{'''}} + 2 y^{^{''}} = 32 e^{2 x} + 24 x

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

Solution steps

y^{'''} (x) + 2 y^{''} (x) = 32 e^{2 x} + 24 x

Solve linear ODE:

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

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

y^{^{''}} - 4 y^{^{'}} + 3 y = 4 e^{3 x}

y^{^{'''}} - 4 y^{^{''}} + y^{^{'}} + 6 y = 8 cos (x) + 18 x + 3

y^{^{''}} + y = sin (t), y (0) = 1, y^{^{'}} (0) = - 1

y^{^{''}} + 3 y^{^{'}} + 2 y = sec^{2} (e^{x})

3 y^{^{''}} + y^{^{'}} - 2 y = x^{2} - 3 x + 7

What is the solution for y^{'''}+2y^{''}=32e^{2x}+24x ?
The solution for y^{'''}+2y^{''}=32e^{2x}+24x is y=c_{1}e^{-2x}+c_{2}+c_{3}x+2e^{2x}+2x^3-3x^2