Internal problem ID [11298]
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)]`]]
\[ \boxed {\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x +4 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 50
dsolve((1-x^2)*diff(y(x),x$2)-x*diff(y(x),x)+4*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (8 x^{3}-4 x \right ) c_{2} \sqrt {x^{2}-1}+\left (8 x^{4}-8 x^{2}+1\right ) c_{2} +c_{1}}{\left (x +\sqrt {x^{2}-1}\right )^{2}} \]
✓ Solution by Mathematica
Time used: 0.316 (sec). Leaf size: 97
DSolve[(1-x^2)*y''[x]-x*y'[x]+4*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 \cosh \left (\frac {4 \sqrt {1-x^2} \arctan \left (\frac {\sqrt {1-x^2}}{x+1}\right )}{\sqrt {x^2-1}}\right )-i c_2 \sinh \left (\frac {4 \sqrt {1-x^2} \arctan \left (\frac {\sqrt {1-x^2}}{x+1}\right )}{\sqrt {x^2-1}}\right ) \]