y^{''}-(6/x)y^'-(9/(x^2))y=0

Lösung

y^{^{''}} - (\frac{6}{x}) y^{^{'}} - (\frac{9}{x ^{2}}) y = 0

y = c_{1} x^{\frac{7 + 85}{2}} + c_{2} x^{\frac{7 - 85}{2}}

Schritte zur Lösung

y^{''} (x) - (\frac{6}{x}) y^{'} (x) - (\frac{9}{x ^{2}}) y = 0

Solve linear ODE:

y = c_{1} x^{\frac{7 + 85}{2}} + c_{2} x^{\frac{7 - 85}{2}}

y = c_{1} x^{\frac{7 + 85}{2}} + c_{2} x^{\frac{7 - 85}{2}}

x \to - 2 + lim (\frac{- 2}{x ^{2} - 4})

x \to + 0 lim (\frac{1}{x})

x^{^{''}} + k x^{^{'}} + x = 0

\frac{d}{d x} (\frac{3 x ^{2}}{4})

x \to 0 + lim (cot (4 x))