Internal problem ID [10319]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IX, Miscellaneous methods for solving equations of higher order than first. Article 62.
Summary. Page 144
Problem number: Ex 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {\left (-x^{2}+1\right ) y^{\prime \prime }-y^{\prime } x -2=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 57
dsolve((1-x^2)*diff(y(x),x$2)-x*diff(y(x),x)=2,y(x), singsol=all)
\[ y \left (x \right ) = \int \frac {-2 \sqrt {x^{2}-1}\, \ln \left (x +\sqrt {x^{2}-1}\right ) \sqrt {x -1}\, \sqrt {x +1}+x^{2} c_{1} -c_{1}}{\left (x -1\right )^{\frac {3}{2}} \left (x +1\right )^{\frac {3}{2}}}d x +c_{2} \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 31
DSolve[(1-x^2)*y''[x]-x*y'[x]==2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2-\frac {1}{4} \left (-2 \text {arctanh}\left (\frac {x}{\sqrt {x^2-1}}\right )+c_1\right ){}^2 \\ \end{align*}