What is the solution for y^{''}+y^'=e^xcos(x) ?

The solution for y^{''}+y^'=e^xcos(x) is y=c_{1}+c_{2}e^{-x}+3/10 e^xsin(x)+1/10 e^xcos(x)

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y^{''}+y^'=e^xcos(x)

y^{^{''}} + y^{^{'}} = e^{x} cos (x)

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

Solution steps

y^{''} (x) + y^{'} (x) = e^{x} cos (x)

Solve linear ODE:

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

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

(d - 1)^{3} y = e^{x} + 5^{x} - 1

y^{^{''}} + 2 y^{^{'}} - 3 y = e^{- 3 x}

y^{^{''}} - 2 y^{^{'}} + y = 12 e^{3 t}, y (0) = - 1, y^{^{'}} (0) = 0

2 y^{^{''}} - 4 y^{^{'}} + 2 y = e^{x} x^{- 1}

\frac{d ^{2} y}{d x ^{2}} - 5 \frac{d y}{d x} + 6 y = x^{2}

What is the solution for y^{''}+y^'=e^xcos(x) ?
The solution for y^{''}+y^'=e^xcos(x) is y=c_{1}+c_{2}e^{-x}+3/10 e^xsin(x)+1/10 e^xcos(x)