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

The solution for y^{''}= 1/(x^2)y is y=c_{1}x^{(1+sqrt(5))/2}+c_{2}x^{(1-sqrt(5))/2}

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

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

y = c_{1} x^{\frac{1 + 5}{2}} + c_{2} x^{\frac{1 - 5}{2}}

Solution steps

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

Solve linear ODE:

y = c_{1} x^{\frac{1 + 5}{2}} + c_{2} x^{\frac{1 - 5}{2}}

y = c_{1} x^{\frac{1 + 5}{2}} + c_{2} x^{\frac{1 - 5}{2}}

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What is the solution for y^{''}= 1/(x^2)y ?
The solution for y^{''}= 1/(x^2)y is y=c_{1}x^{(1+sqrt(5))/2}+c_{2}x^{(1-sqrt(5))/2}