What is the solution for y^{''}+y^'=e^{2x}sin(x) ?

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

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y^{''}+y^'=e^{2x}sin(x)

y^{^{''}} + y^{^{'}} = e^{2 x} sin (x)

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

Solution steps

y^{''} (x) + y^{'} (x) = e^{2 x} sin (x)

Solve linear ODE:

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

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

y^{^{''}} + y^{^{'}} + y = e^{x}

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

y^{^{''}} + 5 y = 3 cos (2 t)

y^{^{''}} + 4 y^{^{'}} = x^{2} + 3 x + 4

\frac{d ^{2} y}{d x ^{2}} - \frac{1}{5} \frac{d y}{d x} + \frac{3}{400} = 0

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