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}}

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)