What is the solution for y^{'''}-y^'=3-7t ?

The solution for y^{'''}-y^'=3-7t is y=c_{1}+c_{2}e^{-t}+c_{3}e^t+(7t^2)/2-3t

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y^{'''}-y^'=3-7t

y^{^{'''}} - y^{^{'}} = 3 - 7 t

y = c_{1} + c_{2} e^{- t} + c_{3} e^{t} + \frac{7 t ^{2}}{2} - 3 t

Solution steps

y^{'''} (t) - y^{'} (t) = 3 - 7 t

Solve linear ODE:

y = c_{1} + c_{2} e^{- t} + c_{3} e^{t} + \frac{7 t ^{2}}{2} - 3 t

y = c_{1} + c_{2} e^{- t} + c_{3} e^{t} + \frac{7 t ^{2}}{2} - 3 t

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

y^{^{''}} + 6 y^{^{'}} + 9 y = e^{- 3 t} ln (t)

y^{^{'''}} - 5 y^{^{''}} - y^{^{'}} + 5 y = e^{4 x}

(D^{2} - D) y = 2 - 2 x

y^{^{''}} - 6 y^{^{'}} + 8 y = x, y (0) = 0, y^{^{'}} (0) = 0

What is the solution for y^{'''}-y^'=3-7t ?
The solution for y^{'''}-y^'=3-7t is y=c_{1}+c_{2}e^{-t}+c_{3}e^t+(7t^2)/2-3t