What is the solution for y^{''}+3y=e^{2x} ?

The solution for y^{''}+3y=e^{2x} is y=c_{1}cos(sqrt(3)x)+c_{2}sin(sqrt(3)x)+1/7 e^{2x}

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

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

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{1}{7} e^{2 x}

Solution steps

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

Solve linear ODE:

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{1}{7} e^{2 x}

y = c_{1} cos (3 x) + c_{2} sin (3 x) + \frac{1}{7} e^{2 x}

y^{^{'''}} + 3 y^{^{'}} = sin (x) + 1

y^{^{''}} - 4 y = 12 t^{2} cos^{2} (t)

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

2 x^{^{''}} + 4 x^{^{'}} + 128 x = cos (3 t)

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

What is the solution for y^{''}+3y=e^{2x} ?
The solution for y^{''}+3y=e^{2x} is y=c_{1}cos(sqrt(3)x)+c_{2}sin(sqrt(3)x)+1/7 e^{2x}