What is the solution for y^{''}+2y^'+y=12e-t ?

The solution for y^{''}+2y^'+y=12e-t is y=c_{1}e^{-t}+c_{2}te^{-t}-t+12e+2

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y^{''}+2y^'+y=12e-t

y^{^{''}} + 2 y^{^{'}} + y = 12 e - t

y = c_{1} e^{- t} + c_{2} t e^{- t} - t + 12 e + 2

Solution steps

y^{''} (t) + 2 y^{'} (t) + y = 12 e - t

Solve linear ODE:

y = c_{1} e^{- t} + c_{2} t e^{- t} - t + 12 e + 2

y = c_{1} e^{- t} + c_{2} t e^{- t} - t + 12 e + 2

\int csc^{2} (θ) - 1 d θ

\int - e^{x^{2}} d x

\frac{d}{d x} ((4 x - 3)^{8})

t^{2} + 4

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

What is the solution for y^{''}+2y^'+y=12e-t ?
The solution for y^{''}+2y^'+y=12e-t is y=c_{1}e^{-t}+c_{2}te^{-t}-t+12e+2