What is the solution for y^{''}-2y^'-3y=3x-4 ?

The solution for y^{''}-2y^'-3y=3x-4 is y=c_{1}e^{3x}+c_{2}e^{-x}-x+2

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y^{''}-2y^'-3y=3x-4

y^{^{''}} - 2 y^{^{'}} - 3 y = 3 x - 4

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

Solution steps

y^{''} (x) - 2 y^{'} (x) - 3 y = 3 x - 4

Solve linear ODE:

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

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

What is the solution for y^{''}-2y^'-3y=3x-4 ?
The solution for y^{''}-2y^'-3y=3x-4 is y=c_{1}e^{3x}+c_{2}e^{-x}-x+2