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

The solution for y^{''}-y=te^t is y=c_{1}e^t+c_{2}e^{-t}+(e^tt^2)/4-(e^tt)/4

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

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

y = c_{1} e^{t} + c_{2} e^{- t} + \frac{e ^{t} t ^{2}}{4} - \frac{e ^{t} t}{4}

Solution steps

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

Solve linear ODE:

y = c_{1} e^{t} + c_{2} e^{- t} + \frac{e ^{t} t ^{2}}{4} - \frac{e ^{t} t}{4}

y = c_{1} e^{t} + c_{2} e^{- t} + \frac{e ^{t} t ^{2}}{4} - \frac{e ^{t} t}{4}

\frac{\partial}{\partial x} (x^{2} + 1)

f (x) = 2 x e^{x} cos (x), at x = 0

\int_{0}^{2} sin (x) + e^{x} d x

What is the solution for y^{''}-y=te^t ?
The solution for y^{''}-y=te^t is y=c_{1}e^t+c_{2}e^{-t}+(e^tt^2)/4-(e^tt)/4