What is the solution for y^{''}+4y^'=10t+1 ?

The solution for y^{''}+4y^'=10t+1 is y=c_{1}+c_{2}e^{-4t}+(5t^2)/4-(3t)/8

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y^{''}+4y^'=10t+1

y^{^{''}} + 4 y^{^{'}} = 10 t + 1

y = c_{1} + c_{2} e^{- 4 t} + \frac{5 t ^{2}}{4} - \frac{3 t}{8}

Solution steps

y^{''} (t) + 4 y^{'} (t) = 10 t + 1

Solve linear ODE:

y = c_{1} + c_{2} e^{- 4 t} + \frac{5 t ^{2}}{4} - \frac{3 t}{8}

y = c_{1} + c_{2} e^{- 4 t} + \frac{5 t ^{2}}{4} - \frac{3 t}{8}

What is the solution for y^{''}+4y^'=10t+1 ?
The solution for y^{''}+4y^'=10t+1 is y=c_{1}+c_{2}e^{-4t}+(5t^2)/4-(3t)/8