60.1.483 problem 486

Internal problem ID [10497]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 486
Date solved : Monday, January 27, 2025 at 08:21:15 PM
CAS classification : [_quadrature]

\begin{align*} y^{2} {y^{\prime }}^{2}+y^{2}-a^{2}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.089 (sec). Leaf size: 54

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

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

✓ Solution by Mathematica

Time used: 0.218 (sec). Leaf size: 101

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

\begin{align*} y(x)\to -\sqrt {a^2-(x+c_1){}^2} \\ y(x)\to \sqrt {a^2-(x+c_1){}^2} \\ y(x)\to -\sqrt {a^2-(x-c_1){}^2} \\ y(x)\to \sqrt {a^2-(x-c_1){}^2} \\ y(x)\to -a \\ y(x)\to a \\ \end{align*}