What is the solution for y^{''}+y^'=e^t*cos(t) ?

The solution for y^{''}+y^'=e^t*cos(t) is y=c_{1}+c_{2}e^{-t}+3/10 e^tsin(t)+1/10 e^tcos(t)

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

y^{^{''}} + y^{^{'}} = e^{t} \cdot cos (t)

y = c_{1} + c_{2} e^{- t} + \frac{3}{10} e^{t} sin (t) + \frac{1}{10} e^{t} cos (t)

Solution steps

y^{''} (t) + y^{'} (t) = e^{t} \cdot cos (t)

Solve linear ODE:

y = c_{1} + c_{2} e^{- t} + \frac{3}{10} e^{t} sin (t) + \frac{1}{10} e^{t} cos (t)

y = c_{1} + c_{2} e^{- t} + \frac{3}{10} e^{t} sin (t) + \frac{1}{10} e^{t} cos (t)

What is the solution for y^{''}+y^'=e^t*cos(t) ?
The solution for y^{''}+y^'=e^t*cos(t) is y=c_{1}+c_{2}e^{-t}+3/10 e^tsin(t)+1/10 e^tcos(t)