What is the solution for 2y^{''}+y=9e^{2x} ?

The solution for 2y^{''}+y=9e^{2x} is y=c_{1}cos(x/(sqrt(2)))+c_{2}sin(x/(sqrt(2)))+e^{2x}

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

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

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

Solution steps

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

Solve linear ODE:

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

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

What is the solution for 2y^{''}+y=9e^{2x} ?
The solution for 2y^{''}+y=9e^{2x} is y=c_{1}cos(x/(sqrt(2)))+c_{2}sin(x/(sqrt(2)))+e^{2x}