What is the solution for x^2y^{''}+xy^'-9y=x^3+1 ?

The solution for x^2y^{''}+xy^'-9y=x^3+1 is y=c_{1}x^3+(c_{2})/(x^3)+(6x^3ln(x)-x^3-4)/(36)

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x^2y^{''}+xy^'-9y=x^3+1

x^{2} y^{^{''}} + x y^{^{'}} - 9 y = x^{3} + 1

y = c_{1} x^{3} + \frac{c _{2}}{x ^{3}} + \frac{6 x ^{3} ln ( x ) - x ^{3} - 4}{36}

Solution steps

x^{2} y^{''} (x) + x y^{'} (x) - 9 y = x^{3} + 1

Solve linear ODE:

y = c_{1} x^{3} + \frac{c _{2}}{x ^{3}} + \frac{6 x ^{3} ln ( x ) - x ^{3} - 4}{36}

y = c_{1} x^{3} + \frac{c _{2}}{x ^{3}} + \frac{6 x ^{3} ln ( x ) - x ^{3} - 4}{36}

n = 0 \sum \infty (1 + \frac{2}{n})^{3 n}

\frac{d}{d x} (x^{a} (1 - x)^{b})

x \to - 8 lim (\frac{- 5 x}{x + 8})

\int \frac{v}{0.122 - 0.0007 v ^{2}} d v

\int \frac{9 x ^{2} - 49}{x ^{3}} d x

What is the solution for x^2y^{''}+xy^'-9y=x^3+1 ?
The solution for x^2y^{''}+xy^'-9y=x^3+1 is y=c_{1}x^3+(c_{2})/(x^3)+(6x^3ln(x)-x^3-4)/(36)