What is the solution for y^{''}-3y^'=8x ?

The solution for y^{''}-3y^'=8x is y=c_{1}e^{3x}+c_{2}-(4x^2)/3-(8x)/9

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y^{''}-3y^'=8x

y^{^{''}} - 3 y^{^{'}} = 8 x

y = c_{1} e^{3 x} + c_{2} - \frac{4 x ^{2}}{3} - \frac{8 x}{9}

Solution steps

y^{''} (x) - 3 y^{'} (x) = 8 x

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} - \frac{4 x ^{2}}{3} - \frac{8 x}{9}

y = c_{1} e^{3 x} + c_{2} - \frac{4 x ^{2}}{3} - \frac{8 x}{9}

x \to 4 + lim (\frac{x}{x - 4})

\frac{1}{3 s + 2}

\frac{d ^{2}}{d x ^{2}} (\frac{x ^{2}}{1 + x})

\frac{5 x}{x + 2}

7 x^{3}

What is the solution for y^{''}-3y^'=8x ?
The solution for y^{''}-3y^'=8x is y=c_{1}e^{3x}+c_{2}-(4x^2)/3-(8x)/9