What is the solution for y^{''}-2y^'+5y=e^{2x} ?

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

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y^{''}-2y^'+5y=e^{2x}

y^{^{''}} - 2 y^{^{'}} + 5 y = e^{2 x}

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

Solution steps

y^{''} (x) - 2 y^{'} (x) + 5 y = e^{2 x}

Solve linear ODE:

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

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

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