What is the solution for y^{''}+y=5e^{-7t} ?

The solution for y^{''}+y=5e^{-7t} is y=c_{1}cos(t)+c_{2}sin(t)+1/10 e^{-7t}

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y^{''}+y=5e^{-7t}

y^{^{''}} + y = 5 e^{- 7 t}

y = c_{1} cos (t) + c_{2} sin (t) + \frac{1}{10} e^{- 7 t}

Solution steps

y^{''} (t) + y = 5 e^{- 7 t}

Solve linear ODE:

y = c_{1} cos (t) + c_{2} sin (t) + \frac{1}{10} e^{- 7 t}

y = c_{1} cos (t) + c_{2} sin (t) + \frac{1}{10} e^{- 7 t}

e^{- 5 t} sin (2 t)

\int - x^{2} + 4 x d x

(2 x y - sec^{2} (x)) d x + (x^{2} + 2 y) d y = 0

\int 2^{s i n^{2} (\frac{1}{3}) x} sin (\frac{2}{3}) x d x

What is the solution for y^{''}+y=5e^{-7t} ?
The solution for y^{''}+y=5e^{-7t} is y=c_{1}cos(t)+c_{2}sin(t)+1/10 e^{-7t}