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

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

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

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

y = c_{1} cos (t) + c_{2} sin (t) + \frac{e ^{t} t}{2} - \frac{1}{2} e^{t}

Solution steps

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

Solve linear ODE:

y = c_{1} cos (t) + c_{2} sin (t) + \frac{e ^{t} t}{2} - \frac{1}{2} e^{t}

y = c_{1} cos (t) + c_{2} sin (t) + \frac{e ^{t} t}{2} - \frac{1}{2} e^{t}

\frac{d}{d x} (x y z)

\int_{\frac{1}{2}}^{1} (x^{- 3} - 12) d x

x \to 1 + lim (\frac{2}{x - 1})

f (x) = \frac{x ^{2}}{4}

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

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