What is the solution for y^{''}-(4/x)y^'-(8/(x^2))y=0 ?

The solution for y^{''}-(4/x)y^'-(8/(x^2))y=0 is y=c_{1}x^{(5+sqrt(57))/2}+c_{2}x^{(5-sqrt(57))/2}

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y^{''}-(4/x)y^'-(8/(x^2))y=0

y^{^{''}} - (\frac{4}{x}) y^{^{'}} - (\frac{8}{x ^{2}}) y = 0

y = c_{1} x^{\frac{5 + 57}{2}} + c_{2} x^{\frac{5 - 57}{2}}

Solution steps

y^{''} (x) - (\frac{4}{x}) y^{'} (x) - (\frac{8}{x ^{2}}) y = 0

Solve linear ODE:

y = c_{1} x^{\frac{5 + 57}{2}} + c_{2} x^{\frac{5 - 57}{2}}

y = c_{1} x^{\frac{5 + 57}{2}} + c_{2} x^{\frac{5 - 57}{2}}

\int x (4 - 2 x^{2}) d x

y = \frac{6}{x ^{4}} - \frac{4}{x ^{2}} - \frac{3}{x}

\frac{\partial}{\partial x} (x^{2} e^{\frac{y}{x}})

\int 9 x^{2} - 4 x + 1 d x

\int π e^{x} d x

What is the solution for y^{''}-(4/x)y^'-(8/(x^2))y=0 ?
The solution for y^{''}-(4/x)y^'-(8/(x^2))y=0 is y=c_{1}x^{(5+sqrt(57))/2}+c_{2}x^{(5-sqrt(57))/2}