Internal problem ID [5106]
Book: THEORY OF DIFFERENTIAL EQUATIONS IN ENGINEERING AND MECHANICS. K.T.
CHAU, CRC Press. Boca Raton, FL. 2018
Section: Chapter 3. Ordinary Differential Equations. Section 3.5 HIGHER ORDER ODE. Page
181
Problem number: Example 3.32.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [_Gegenbauer, [_2nd_order, _linear, _with_symmetry_[0,F(x)]]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-\frac {x y^{\prime }}{-x^{2}+1}+\frac {y}{-x^{2}+1}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 20
dsolve(diff(y(x),x$2)-x/(1-x^2)*diff(y(x),x)+y(x)/(1-x^2)=0,y(x), singsol=all)
\[ y \relax (x ) = c_{1} x +c_{2} \sqrt {x -1}\, \sqrt {x +1} \]
✓ Solution by Mathematica
Time used: 0.057 (sec). Leaf size: 63
DSolve[y''[x]-x/(1-x^2)*y'[x]+y[x]/(1-x^2)==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cosh \left (\frac {\sqrt {1-x^2} \text {ArcSin}(x)}{\sqrt {x^2-1}}\right )+i c_2 \sinh \left (\frac {\sqrt {1-x^2} \text {ArcSin}(x)}{\sqrt {x^2-1}}\right ) \\ \end{align*}