60.3.233 problem 1238

Internal problem ID [11243]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1238
Date solved : Monday, January 27, 2025 at 10:49:48 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 26

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

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

✓ Solution by Mathematica

Time used: 17.407 (sec). Leaf size: 31

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

\[ y(x)\to \int _1^x\frac {c_1+a K[1]}{K[1]^2-1}dK[1]+c_2 \]