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

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

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

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

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

Solution steps

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

Solve linear ODE:

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

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

y^{^{''}} + 25 y = x^{2}

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

5 y^{^{''}} + 6 y^{^{'}} + \frac{5}{1.96} y = 3 cos (2 t)

y^{^{''}} + 200 y^{^{'}} + 1000000 = 0

f^{^{''}} (t) + f (t) = cos (t)

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