62.17.1 problem Ex 1

Internal problem ID [12901]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IV, differential equations of the first order and higher degree than the first. Article 28. Summary. Page 59
Problem number : Ex 1
Date solved : Tuesday, January 28, 2025 at 04:40:47 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.125 (sec). Leaf size: 54

dsolve(y(x)^2*(1+diff(y(x),x)^2)=a^2,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: 0.235 (sec). Leaf size: 101

DSolve[y[x]^2*(1+(D[y[x],x])^2)==a^2,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*}