What is the solution for y^{''}-5y^'-50y=5+3t ?

The solution for y^{''}-5y^'-50y=5+3t is y=c_{1}e^{10t}+c_{2}e^{-5t}-(3t)/(50)-47/500

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y^{''}-5y^'-50y=5+3t

y^{^{''}} - 5 y^{^{'}} - 50 y = 5 + 3 t

y = c_{1} e^{10 t} + c_{2} e^{- 5 t} - \frac{3 t}{50} - \frac{47}{500}

Solution steps

y^{''} (t) - 5 y^{'} (t) - 50 y = 5 + 3 t

Solve linear ODE:

y = c_{1} e^{10 t} + c_{2} e^{- 5 t} - \frac{3 t}{50} - \frac{47}{500}

y = c_{1} e^{10 t} + c_{2} e^{- 5 t} - \frac{3 t}{50} - \frac{47}{500}

What is the solution for y^{''}-5y^'-50y=5+3t ?
The solution for y^{''}-5y^'-50y=5+3t is y=c_{1}e^{10t}+c_{2}e^{-5t}-(3t)/(50)-47/500