What is the solution for y^{''}-3y^'+2y=-2x ?

The solution for y^{''}-3y^'+2y=-2x is y=c_{1}e^{2x}+c_{2}e^x-x-3/2

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y^{''}-3y^'+2y=-2x

y^{^{''}} - 3 y^{^{'}} + 2 y = - 2 x

y = c_{1} e^{2 x} + c_{2} e^{x} - x - \frac{3}{2}

Solution steps

y^{''} (x) - 3 y^{'} (x) + 2 y = - 2 x

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} - x - \frac{3}{2}

y = c_{1} e^{2 x} + c_{2} e^{x} - x - \frac{3}{2}

What is the solution for y^{''}-3y^'+2y=-2x ?
The solution for y^{''}-3y^'+2y=-2x is y=c_{1}e^{2x}+c_{2}e^x-x-3/2