What is the solution for x^2y^{''}+2xy^'-6y=0 ?

The solution for x^2y^{''}+2xy^'-6y=0 is y=c_{1}x^2+(c_{2})/(x^3)

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x^2y^{''}+2xy^'-6y=0

x^{2} y^{^{''}} + 2 x y^{^{'}} - 6 y = 0

y = c_{1} x^{2} + \frac{c _{2}}{x ^{3}}

Solution steps

x^{2} y^{''} (x) + 2 x y^{'} (x) - 6 y = 0

Solve linear ODE:

y = c_{1} x^{2} + \frac{c _{2}}{x ^{3}}

y = c_{1} x^{2} + \frac{c _{2}}{x ^{3}}

x \to - 2 - lim (\frac{1}{( x + 2 ) ^{5}})

\frac{d}{d x} (3 x^{6} e^{x})

x + 4 y = 25, x + 7 = y^{2}

\int \frac{1}{x ^{2}} 4 + \frac{1}{x} d x

- 2 x^{3} (x^{2} + 1)^{- 2}

What is the solution for x^2y^{''}+2xy^'-6y=0 ?
The solution for x^2y^{''}+2xy^'-6y=0 is y=c_{1}x^2+(c_{2})/(x^3)