Internal problem ID [10842]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 2, DIFFERENTIAL EQUATIONS OF THE SECOND ORDER AND HIGHER.
Problems page 172
Problem number: Problem 36.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}-1\right ) y^{\prime \prime }-6 y-1=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 54
dsolve((x^2-1)*diff(y(x),x$2)-6*y(x)=1,y(x), singsol=all)
\[ y \left (x \right ) = \left (x^{3}-x \right ) c_{2} +\left (\frac {\left (3 x^{3}-3 x \right ) \ln \left (x -1\right )}{4}+\frac {\left (-3 x^{3}+3 x \right ) \ln \left (x +1\right )}{4}+\frac {3 x^{2}}{2}-1\right ) c_{1} -\frac {1}{6} \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 43
DSolve[(x^2-1)*y''[x]-6*y[x]==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {3}{2} c_2 \left (x^2-1\right ) x \text {arctanh}(x)-\frac {3 c_2 x^2}{2}+c_1 \left (x^2-1\right ) x-\frac {1}{6}+c_2 \\ \end{align*}