66.2.27 problem Problem 36

Internal problem ID [13926]
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
Date solved : Tuesday, January 28, 2025 at 06:08:55 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} \left (x^{2}-1\right ) y^{\prime \prime }-6 y&=1 \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 52

dsolve((x^2-1)*diff(y(x),x$2)-6*y(x)=1,y(x), singsol=all)
 

\[ y = -\frac {1}{6}+\frac {3 \left (x^{3}-x \right ) c_{1} \ln \left (x -1\right )}{4}+\frac {3 c_{1} \left (-x^{3}+x \right ) \ln \left (x +1\right )}{4}+c_{2} x^{3}+\frac {3 c_{1} x^{2}}{2}-c_{2} x -c_{1} \]

✓ Solution by Mathematica

Time used: 0.069 (sec). Leaf size: 67

DSolve[(x^2-1)*D[y[x],{x,2}]-6*y[x]==1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{12} \left (-9 c_2 x \left (x^2-1\right ) \log (1-x)+9 c_2 x \left (x^2-1\right ) \log (x+1)+2 \left (6 c_1 x^3-9 c_2 x^2-6 c_1 x-1+6 c_2\right )\right ) \]