What is the solution for y^{''}-4y^'+13y=2e^x ?

The solution for y^{''}-4y^'+13y=2e^x is y=e^{2x}(c_{1}cos(3x)+c_{2}sin(3x))+1/5 e^x

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y^{''}-4y^'+13y=2e^x

y^{^{''}} - 4 y^{^{'}} + 13 y = 2 e^{x}

y = e^{2 x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{1}{5} e^{x}

Solution steps

y^{''} (x) - 4 y^{'} (x) + 13 y = 2 e^{x}

Solve linear ODE:

y = e^{2 x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{1}{5} e^{x}

y = e^{2 x} (c_{1} cos (3 x) + c_{2} sin (3 x)) + \frac{1}{5} e^{x}

What is the solution for y^{''}-4y^'+13y=2e^x ?
The solution for y^{''}-4y^'+13y=2e^x is y=e^{2x}(c_{1}cos(3x)+c_{2}sin(3x))+1/5 e^x