What is the solution for y^{''}-3y=e^{2x}sin(x) ?

The solution for y^{''}-3y=e^{2x}sin(x) is y=c_{1}e^{sqrt(3)x}+c_{2}e^{-sqrt(3)x}-1/4 e^{2x}cos(x)

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y^{''}-3y=e^{2x}sin(x)

y^{^{''}} - 3 y = e^{2 x} sin (x)

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{1}{4} e^{2 x} cos (x)

Solution steps

y^{''} (x) - 3 y = e^{2 x} sin (x)

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{1}{4} e^{2 x} cos (x)

y = c_{1} e^{3 x} + c_{2} e^{- 3 x} - \frac{1}{4} e^{2 x} cos (x)

y^{^{''}} + 9 y = e^{2 x}

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

y^{^{''}} - y = sin (t), y (0) = 0, y^{^{'}} (0) = 1

y^{^{''}} + 6 y^{^{'}} + 9 y = 2 sin (x)

y^{^{''}} - 8 y^{^{'}} + 16 y = 8 e^{4 x}

What is the solution for y^{''}-3y=e^{2x}sin(x) ?
The solution for y^{''}-3y=e^{2x}sin(x) is y=c_{1}e^{sqrt(3)x}+c_{2}e^{-sqrt(3)x}-1/4 e^{2x}cos(x)