60.3.232 problem 1237

Internal problem ID [11242]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1237
Date solved : Monday, January 27, 2025 at 10:49:46 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 20

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

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

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 26

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

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