y'' + y/x^6=0
You asked:
Investigate the equation: \(y^{\prime \prime} + \frac{y}{{x}^{6}} = 0\).
MathBot Answer:
\[y{\left(x \right)} = \sqrt{x} \left(C_{2} Y_{- \frac{1}{4}}\left(- \frac{1}{2 x^{2}}\right) + \frac{\sqrt[4]{\frac{1}{x^{2}}} C_{1} J_{- \frac{1}{4}}\left(\frac{1}{2 x^{2}}\right)}{\sqrt[4]{- \frac{1}{x^{2}}}}\right)\]
\(C_{1}\), \(C_{2}\) are arbitrary constants.