What is the solution for y^{''}-y=-15t+5 ?

The solution for y^{''}-y=-15t+5 is y=c_{1}e^t+c_{2}e^{-t}+15t-5

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y^{''}-y=-15t+5

y^{^{''}} - y = - 15 t + 5

y = c_{1} e^{t} + c_{2} e^{- t} + 15 t - 5

Solution steps

y^{''} (t) - y = - 15 t + 5

Solve linear ODE:

y = c_{1} e^{t} + c_{2} e^{- t} + 15 t - 5

y = c_{1} e^{t} + c_{2} e^{- t} + 15 t - 5

y^{^{''}} + 6 y^{^{'}} + 5 y = 12 e^{x}, y (0) = - 1, y^{^{'}} (0) = 7

y^{^{''}} - 2 y^{^{'}} + y = 3 t + 1 e^{- t}

2 y^{^{''}} + 14 y^{^{'}} + 12 y = 0.7

0.25 y^{^{''}} + 10 y^{^{'}} + 1000 = 0

y^{^{''}} - 12 y^{^{'}} + 36 y = 280 sin (x) - 184 cos (x)

What is the solution for y^{''}-y=-15t+5 ?
The solution for y^{''}-y=-15t+5 is y=c_{1}e^t+c_{2}e^{-t}+15t-5