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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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

y^{^{''}} - 2 y^{^{'}} + y = - x + 2 + 2 cos (x)

y^{^{''}} + y^{^{'}} + y = 5 x + 3

y^{^{''}} + 5 y^{^{'}} + 6 y = 3 e^{- 2 t}

y^{^{'''}} - 2 y^{^{''}} - 21 y^{^{'}} - 18 y = 3 + 4 e^{- t}

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