What is the solution for y^{''}-6y^'+8y=e^{2x} ?

The solution for y^{''}-6y^'+8y=e^{2x} is y=c_{1}e^{4x}+c_{2}e^{2x}-(e^{2x}x)/2

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y^{''}-6y^'+8y=e^{2x}

y^{^{''}} - 6 y^{^{'}} + 8 y = e^{2 x}

y = c_{1} e^{4 x} + c_{2} e^{2 x} - \frac{e ^{2 x} x}{2}

Solution steps

y^{''} (x) - 6 y^{'} (x) + 8 y = e^{2 x}

Solve linear ODE:

y = c_{1} e^{4 x} + c_{2} e^{2 x} - \frac{e ^{2 x} x}{2}

y = c_{1} e^{4 x} + c_{2} e^{2 x} - \frac{e ^{2 x} x}{2}

What is the solution for y^{''}-6y^'+8y=e^{2x} ?
The solution for y^{''}-6y^'+8y=e^{2x} is y=c_{1}e^{4x}+c_{2}e^{2x}-(e^{2x}x)/2