Internal problem ID [8818]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 2, linear second order
Problem number: 1238.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
Solve \begin {gather*} \boxed {\left (x^{2}-1\right ) y^{\prime \prime }+2 x y^{\prime }-a=0} \end {gather*}
✓ Solution by Maple
Time used: 0.001 (sec). Leaf size: 34
dsolve((x^2-1)*diff(diff(y(x),x),x)+2*x*diff(y(x),x)-a=0,y(x), singsol=all)
\[ y \relax (x ) = \frac {\ln \left (x -1\right ) c_{1}}{2}+\frac {a \ln \left (x -1\right )}{2}-\frac {c_{1} \ln \left (x +1\right )}{2}+\frac {a \ln \left (x +1\right )}{2}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.049 (sec). Leaf size: 35
DSolve[-a + 2*x*y'[x] + (-1 + x^2)*y''[x] == 0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} ((a+c_1) \log (1-x)+(a-c_1) \log (x+1))+c_2 \\ \end{align*}