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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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