29.31.22 problem 921

Internal problem ID [5501]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 31
Problem number : 921
Date solved : Monday, January 27, 2025 at 11:32:55 AM
CAS classification : [_separable]

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

✓ Solution by Maple

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

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

\begin{align*} y \left (x \right ) &= \frac {c_{1}}{-x +a} \\ y \left (x \right ) &= \frac {c_{1}}{x +a} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.054 (sec). Leaf size: 32

DSolve[(a^2-x^2) (D[y[x],x])^2-2 x y[x] D[y[x],x]-y[x]^2==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \frac {c_1}{a-x} \\ y(x)\to \frac {c_1}{a+x} \\ y(x)\to 0 \\ \end{align*}