Link to actual problem [9894] \[ \boxed {\left (x^{2}-1\right )^{2} y^{\prime \prime \prime \prime }+10 x \left (x^{2}-1\right ) y^{\prime \prime \prime }+\left (24 x^{2}-8-2 \left (\mu \left (\mu +1\right )+\nu \left (1+\nu \right )\right ) \left (x^{2}-1\right )\right ) y^{\prime \prime }-6 x \left (\mu \left (\mu +1\right )+\nu \left (1+\nu \right )-2\right ) y^{\prime }+\left (\left (\mu \left (\mu +1\right )-\nu \left (1+\nu \right )\right )^{2}-2 \mu \left (\mu +1\right )-2 \nu \left (1+\nu \right )\right ) y=0} \]
type detected by program
{"unknown"}
type detected by Maple
[[_high_order, _with_linear_symmetries]]
Maple symgen result This shows Maple’s found \(\xi ,\eta \) and the corresponding canonical coordinates \(R,S\)