What is the solution for y^{''}+(y^')/x =2x+1 ?

The solution for y^{''}+(y^')/x =2x+1 is y=c_{1}+c_{2}ln(x)+(8x^3+9x^2)/(36)

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

y^{^{''}} + \frac{y ^{^{'}}}{x} = 2 x + 1

y = c_{1} + c_{2} ln (x) + \frac{8 x ^{3} + 9 x ^{2}}{36}

Solution steps

y^{''} (x) + \frac{y ^{'} ( x )}{x} = 2 x + 1

Solve linear ODE:

y = c_{1} + c_{2} ln (x) + \frac{8 x ^{3} + 9 x ^{2}}{36}

y = c_{1} + c_{2} ln (x) + \frac{8 x ^{3} + 9 x ^{2}}{36}

arctan (x)

y^{^{''}} - 7 y^{^{'}} + 3 y = x e^{x}

x \to 0 lim (\frac{5 x ^{2} - 4 x}{x})

k = 1 \sum \infty \frac{k !}{10 1 ^{k}}

f (x) = 4 x^{2} - 5 x

What is the solution for y^{''}+(y^')/x =2x+1 ?
The solution for y^{''}+(y^')/x =2x+1 is y=c_{1}+c_{2}ln(x)+(8x^3+9x^2)/(36)