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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

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