What is the solution for x^2y^{''}+2xy^'-72y=0 ?

The solution for x^2y^{''}+2xy^'-72y=0 is y=c_{1}x^8+(c_{2})/(x^9)

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x^2y^{''}+2xy^'-72y=0

x^{2} y^{^{''}} + 2 x y^{^{'}} - 72 y = 0

y = c_{1} x^{8} + \frac{c _{2}}{x ^{9}}

Solution steps

x^{2} y^{''} (x) + 2 x y^{'} (x) - 72 y = 0

Solve linear ODE:

y = c_{1} x^{8} + \frac{c _{2}}{x ^{9}}

y = c_{1} x^{8} + \frac{c _{2}}{x ^{9}}

\int_{0}^{2} \frac{x + 1}{x ( x ^{2} + 1 )} d x

y^{^{'}} = \frac{( x - y sin ( 2 x ) )}{sin ^{2} ( x )}

n = 1 \sum \infty \frac{1}{n \cdot 3 ^{n}}

3 e^{- 7 x}

x \to - \infty lim (3 - x)

What is the solution for x^2y^{''}+2xy^'-72y=0 ?
The solution for x^2y^{''}+2xy^'-72y=0 is y=c_{1}x^8+(c_{2})/(x^9)