Internal problem ID [12190]
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]]
\[ \boxed {\left (x^{2}-1\right ) y^{\prime \prime }-6 y=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 52
dsolve((x^2-1)*diff(y(x),x$2)-6*y(x)=1,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {1}{6}+\frac {3 \left (x^{3}-x \right ) c_{1} \ln \left (-1+x \right )}{4}+\frac {3 c_{1} \left (-x^{3}+x \right ) \ln \left (1+x \right )}{4}+c_{2} x^{3}+\frac {3 c_{1} x^{2}}{2}-c_{2} x -c_{1} \]
✓ Solution by Mathematica
Time used: 0.086 (sec). Leaf size: 67
DSolve[(x^2-1)*y''[x]-6*y[x]==1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{12} \left (-9 c_2 x \left (x^2-1\right ) \log (1-x)+9 c_2 x \left (x^2-1\right ) \log (x+1)+2 \left (6 c_1 x^3-9 c_2 x^2-6 c_1 x-1+6 c_2\right )\right ) \]