Internal problem ID [9563]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1234.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {\left (x^{2}-1\right ) y^{\prime \prime }+y^{\prime } x=-2} \]
✓ Solution by Maple
Time used: 0.203 (sec). Leaf size: 59
dsolve((x^2-1)*diff(diff(y(x),x),x)+x*diff(y(x),x)+2=0,y(x), singsol=all)
\[ y \left (x \right ) = -\left (\int -\frac {-2 \sqrt {x^{2}-1}\, \ln \left (x +\sqrt {x^{2}-1}\right ) \sqrt {x -1}\, \sqrt {x +1}+c_{1} \left (x^{2}-1\right )}{\left (x +1\right )^{\frac {3}{2}} \left (x -1\right )^{\frac {3}{2}}}d x \right )+c_{2} \]
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 48
DSolve[2 + x*y'[x] + (-1 + x^2)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2-\frac {1}{4} \left (\log \left (1-\frac {x}{\sqrt {x^2-1}}\right )-\log \left (\frac {x}{\sqrt {x^2-1}}+1\right )+c_1\right ){}^2 \]