Internal problem ID [10284]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VIII, Linear differential equations of the second order. Article 54. Change of
independent variable. Page 127
Problem number: Ex 2.
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 {\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +4 y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve((1-x^2)*diff(y(x),x$2)-x*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {c_{1}}{\left (x +\sqrt {x^{2}-1}\right )^{2}}+c_{2} \left (x +\sqrt {x^{2}-1}\right )^{2} \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 65
DSolve[(1-x^2)*y''[x]-x*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 \cosh \left (\frac {2 \sqrt {1-x^2} \text {ArcSin}(x)}{\sqrt {x^2-1}}\right )+i c_2 \sinh \left (\frac {2 \sqrt {1-x^2} \text {ArcSin}(x)}{\sqrt {x^2-1}}\right ) \\ \end{align*}