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

The solution for y^{''}+2y^'=2t+3 is y=c_{1}+c_{2}e^{-2t}+(t^2)/2+t

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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What is the solution for y^{''}+2y^'=2t+3 ?
The solution for y^{''}+2y^'=2t+3 is y=c_{1}+c_{2}e^{-2t}+(t^2)/2+t