What is the solution for y^{''}-8y^'-4y-2=2x ?

The solution for y^{''}-8y^'-4y-2=2x is y=c_{1}e^{2(2+sqrt(5))x}+c_{2}e^{2(2-sqrt(5))x}-x/2+1/2

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y^{''}-8y^'-4y-2=2x

y^{^{''}} - 8 y^{^{'}} - 4 y - 2 = 2 x

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

Solution steps

y^{''} (x) - 8 y^{'} (x) - 4 y - 2 = 2 x

Solve linear ODE:

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

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

What is the solution for y^{''}-8y^'-4y-2=2x ?
The solution for y^{''}-8y^'-4y-2=2x is y=c_{1}e^{2(2+sqrt(5))x}+c_{2}e^{2(2-sqrt(5))x}-x/2+1/2