What is the solution for y^{''}-y^'-2y=5x+3 ?

The solution for y^{''}-y^'-2y=5x+3 is y=c_{1}e^{2x}+c_{2}e^{-x}-(5x)/2-1/4

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y^{''}-y^'-2y=5x+3

y^{^{''}} - y^{^{'}} - 2 y = 5 x + 3

y = c_{1} e^{2 x} + c_{2} e^{- x} - \frac{5 x}{2} - \frac{1}{4}

Solution steps

y^{''} (x) - y^{'} (x) - 2 y = 5 x + 3

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{- x} - \frac{5 x}{2} - \frac{1}{4}

y = c_{1} e^{2 x} + c_{2} e^{- x} - \frac{5 x}{2} - \frac{1}{4}

6 y^{^{''}} + 6 y^{^{'}} + 73 y = 8 cos (4 x)

\frac{d ^{2} y}{d t ^{2}} + 5 y = 5 sin (t)

\frac{d ^{2} y}{d x ^{2}} - \frac{d y}{d x} - 6 y = - e^{x} + 12 x

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

\frac{1}{2} y^{^{''}} + 2 y = 4 tan (2 t) - \frac{1}{3} e^{t}

What is the solution for y^{''}-y^'-2y=5x+3 ?
The solution for y^{''}-y^'-2y=5x+3 is y=c_{1}e^{2x}+c_{2}e^{-x}-(5x)/2-1/4