What is the solution for y^{''}-7y^'=49t ?

The solution for y^{''}-7y^'=49t is y=c_{1}e^{7t}+c_{2}-(7t^2)/2-t

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y^{''}-7y^'=49t

y^{^{''}} - 7 y^{^{'}} = 49 t

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

Solution steps

y^{''} (t) - 7 y^{'} (t) = 49 t

Solve linear ODE:

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

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

y^{^{''}} = 9 y

\frac{\partial}{\partial y} (2 y x)

\frac{d}{d x} (\frac{- 1}{2 ( x + 1 )})

\int_{- 2}^{3} (x - 5) d x

\int cos^{2} (3 t) d t

What is the solution for y^{''}-7y^'=49t ?
The solution for y^{''}-7y^'=49t is y=c_{1}e^{7t}+c_{2}-(7t^2)/2-t