What is the solution for y^{''}-(2/x)y^'-(7/(x^2))y=0 ?

The solution for y^{''}-(2/x)y^'-(7/(x^2))y=0 is y=c_{1}x^{(3+sqrt(37))/2}+c_{2}x^{(3-sqrt(37))/2}

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y^{''}-(2/x)y^'-(7/(x^2))y=0

y^{^{''}} - (\frac{2}{x}) y^{^{'}} - (\frac{7}{x ^{2}}) y = 0

y = c_{1} x^{\frac{3 + 37}{2}} + c_{2} x^{\frac{3 - 37}{2}}

Solution steps

y^{''} (x) - (\frac{2}{x}) y^{'} (x) - (\frac{7}{x ^{2}}) y = 0

Solve linear ODE:

y = c_{1} x^{\frac{3 + 37}{2}} + c_{2} x^{\frac{3 - 37}{2}}

y = c_{1} x^{\frac{3 + 37}{2}} + c_{2} x^{\frac{3 - 37}{2}}

x \to 1 lim (51 - 2 x)

\frac{d}{d x} (ln (sec (x^{2})))

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\int e^{x + y^{2}} d x

\int_{- 2}^{4} x^{2} (x^{3} + 8)^{2} d x

What is the solution for y^{''}-(2/x)y^'-(7/(x^2))y=0 ?
The solution for y^{''}-(2/x)y^'-(7/(x^2))y=0 is y=c_{1}x^{(3+sqrt(37))/2}+c_{2}x^{(3-sqrt(37))/2}