What is the solution for y^{'''}+2y^{''}=24x^2+24x+4 ?

The solution for y^{'''}+2y^{''}=24x^2+24x+4 is y=c_{1}e^{-2x}+c_{2}+c_{3}x+x^4+x^2

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y^{'''}+2y^{''}=24x^2+24x+4

y^{^{'''}} + 2 y^{^{''}} = 24 x^{2} + 24 x + 4

y = c_{1} e^{- 2 x} + c_{2} + c_{3} x + x^{4} + x^{2}

Solution steps

y^{'''} (x) + 2 y^{''} (x) = 24 x^{2} + 24 x + 4

Solve linear ODE:

y = c_{1} e^{- 2 x} + c_{2} + c_{3} x + x^{4} + x^{2}

y = c_{1} e^{- 2 x} + c_{2} + c_{3} x + x^{4} + x^{2}

y^{^{''}} + 5 y^{^{'}} + 6 y = 8 e^{5 t}

y^{^{'''}} + y^{^{''}} + y^{^{'}} + y = e^{- t} + 6 t

d, d (t) = \frac{( 1 + 16 t ^{2} )}{( 4 t ) ^{3}}

y^{^{''}} - 4 y = 4 t - 8 e^{- 2 t}, y (0) = 0, y^{^{'}} (0) = 5

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

What is the solution for y^{'''}+2y^{''}=24x^2+24x+4 ?
The solution for y^{'''}+2y^{''}=24x^2+24x+4 is y=c_{1}e^{-2x}+c_{2}+c_{3}x+x^4+x^2