What is the solution for y^{''}-6y^'=-2x-5 ?

The solution for y^{''}-6y^'=-2x-5 is y=c_{1}e^{6x}+c_{2}+(x^2)/6+(8x)/9

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y^{''}-6y^'=-2x-5

y^{^{''}} - 6 y^{^{'}} = - 2 x - 5

y = c_{1} e^{6 x} + c_{2} + \frac{x ^{2}}{6} + \frac{8 x}{9}

Solution steps

y^{''} (x) - 6 y^{'} (x) = - 2 x - 5

Solve linear ODE:

y = c_{1} e^{6 x} + c_{2} + \frac{x ^{2}}{6} + \frac{8 x}{9}

y = c_{1} e^{6 x} + c_{2} + \frac{x ^{2}}{6} + \frac{8 x}{9}

\frac{d}{d x} (\frac{3 x}{y})

\int (5 x^{4} - \frac{4}{x ^{4}}) d x

y = (1 - x) (x^{2} - 3)^{2}, (2, - 1)

\frac{1}{1 - x}, 19

\int x^{2} lo g_{3} (x) d x

What is the solution for y^{''}-6y^'=-2x-5 ?
The solution for y^{''}-6y^'=-2x-5 is y=c_{1}e^{6x}+c_{2}+(x^2)/6+(8x)/9