Internal problem ID [5859]
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)]`]]
\[ \boxed {y^{\prime \prime }-\frac {x y^{\prime }}{-x^{2}+1}+\frac {y}{-x^{2}+1}=0} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \left (x \right ) = c_{1} x +c_{2} \sqrt {x -1}\, \sqrt {x +1} \]
✓ Solution by Mathematica
Time used: 0.177 (sec). Leaf size: 97
DSolve[y''[x]-x/(1-x^2)*y'[x]+y[x]/(1-x^2)==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \cosh \left (\frac {2 \sqrt {1-x^2} \arctan \left (\frac {\sqrt {1-x^2}}{x+1}\right )}{\sqrt {x^2-1}}\right )-i c_2 \sinh \left (\frac {2 \sqrt {1-x^2} \arctan \left (\frac {\sqrt {1-x^2}}{x+1}\right )}{\sqrt {x^2-1}}\right ) \]