What is the solution for y^{''}-(2/x)y^'-(3/(x^2))y=0 ?

The solution for y^{''}-(2/x)y^'-(3/(x^2))y=0 is y=c_{1}x^{(3+sqrt(21))/2}+c_{2}x^{(3-sqrt(21))/2}

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y^{''}-(2/x)y^'-(3/(x^2))y=0

y^{^{''}} - (\frac{2}{x}) y^{^{'}} - (\frac{3}{x ^{2}}) y = 0

y = c_{1} x^{\frac{3 + 21}{2}} + c_{2} x^{\frac{3 - 21}{2}}

Solution steps

y^{''} (x) - (\frac{2}{x}) y^{'} (x) - (\frac{3}{x ^{2}}) y = 0

Solve linear ODE:

y = c_{1} x^{\frac{3 + 21}{2}} + c_{2} x^{\frac{3 - 21}{2}}

y = c_{1} x^{\frac{3 + 21}{2}} + c_{2} x^{\frac{3 - 21}{2}}

What is the solution for y^{''}-(2/x)y^'-(3/(x^2))y=0 ?
The solution for y^{''}-(2/x)y^'-(3/(x^2))y=0 is y=c_{1}x^{(3+sqrt(21))/2}+c_{2}x^{(3-sqrt(21))/2}