What is the solution for y^{''}-6y^'=2x+1 ?

The solution for y^{''}-6y^'=2x+1 is y=c_{1}e^{6x}+c_{2}-(x^2)/6-(2x)/9

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y^{''}-6y^'=2x+1

y^{^{''}} - 6 y^{^{'}} = 2 x + 1

y = c_{1} e^{6 x} + c_{2} - \frac{x ^{2}}{6} - \frac{2 x}{9}

Solution steps

y^{''} (x) - 6 y^{'} (x) = 2 x + 1

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} - \frac{x ^{2}}{6} - \frac{2 x}{9}

y = c_{1} e^{6 x} + c_{2} - \frac{x ^{2}}{6} - \frac{2 x}{9}

y^{^{''}} + 3 y^{^{'}} + 2 y = 24 e^{- 2 x}

y^{^{''}} + 100 y = - 2 sin (10 t) - 4 cos (10 t)

(D^{2} + 2 D + 1) y = 2 x + x^{2}

y^{^{''}} + 2 y^{^{'}} + 5 y = 5 H (t)

y^{^{''}} + 3 \cdot y^{^{'}} + 2 \cdot y = x

What is the solution for y^{''}-6y^'=2x+1 ?
The solution for y^{''}-6y^'=2x+1 is y=c_{1}e^{6x}+c_{2}-(x^2)/6-(2x)/9