What is the solution for y^{''}+3y^'+2y=12t^3 ?

The solution for y^{''}+3y^'+2y=12t^3 is y=c_{1}e^{-t}+c_{2}e^{-2t}+6t^3-27t^2+63t-135/2

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y^{''}+3y^'+2y=12t^3

y^{^{''}} + 3 y^{^{'}} + 2 y = 12 t^{3}

y = c_{1} e^{- t} + c_{2} e^{- 2 t} + 6 t^{3} - 27 t^{2} + 63 t - \frac{135}{2}

Solution steps

y^{''} (t) + 3 y^{'} (t) + 2 y = 12 t^{3}

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} e^{- 2 t} + 6 t^{3} - 27 t^{2} + 63 t - \frac{135}{2}

y = c_{1} e^{- t} + c_{2} e^{- 2 t} + 6 t^{3} - 27 t^{2} + 63 t - \frac{135}{2}

(\frac{2}{x ^{3}})^{^{'}}

y = \frac{1}{3} x^{3}

\int e^{- 0.2 x} d x

\int \frac{x}{( x ^{2} + 1 ) ^{\frac{15}{2}}} d x

\int 5 (x^{5} - 10 x)^{2} (x^{4} - 2) d x

What is the solution for y^{''}+3y^'+2y=12t^3 ?
The solution for y^{''}+3y^'+2y=12t^3 is y=c_{1}e^{-t}+c_{2}e^{-2t}+6t^3-27t^2+63t-135/2