60.3.293 problem 1299

Internal problem ID [11303]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 2, linear second order
Problem number : 1299
Date solved : Monday, January 27, 2025 at 11:10:51 PM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 30

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

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