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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

\int \frac{24 q}{4 q ^{2} + 7} d q

\frac{\partial}{\partial x} (2 x^{2} y + 3 x y^{3})

f^{^{'}} (x) = \frac{( 5 x + 1 )}{5 x}

\frac{\partial}{\partial x} (m sin (2 m x + 2 n y))

\int_{0}^{1} 2 x - x^{2} d x

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