48.3.3 problem Example 3.32

Internal problem ID [7527]
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
Date solved : Monday, January 27, 2025 at 03:04:38 PM
CAS classification : [_Gegenbauer, [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} y^{\prime \prime }-\frac {x y^{\prime }}{-x^{2}+1}+\frac {y}{-x^{2}+1}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (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)
 

\[ y = c_{1} x +c_{2} \sqrt {x -1}\, \sqrt {x +1} \]

✓ Solution by Mathematica

Time used: 0.093 (sec). Leaf size: 63

DSolve[D[y[x],{x,2}]-x/(1-x^2)*D[y[x],x]+y[x]/(1-x^2)==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \cosh \left (\frac {\sqrt {1-x^2} \arcsin (x)}{\sqrt {x^2-1}}\right )+i c_2 \sinh \left (\frac {\sqrt {1-x^2} \arcsin (x)}{\sqrt {x^2-1}}\right ) \]