81.2.8 problem 8

Internal problem ID [18616]
Book : A short course on differential equations. By Donald Francis Campbell. Maxmillan company. London. 1907
Section : Chapter II. Change of variable. Exercises at page 20
Problem number : 8
Date solved : Tuesday, January 28, 2025 at 12:04:17 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} \left (-x^{2}+1\right ) y^{\prime \prime }-x y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 18

dsolve((1-x^2)*diff(y(x),x$2)-x*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = c_{1} +\ln \left (x +\sqrt {x^{2}-1}\right ) c_{2} \]

✓ Solution by Mathematica

Time used: 0.015 (sec). Leaf size: 23

DSolve[(1-x^2)*D[y[x],{x,2}]-x*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 \log \left (\sqrt {x^2-1}+x\right )+c_2 \]