Internal problem ID [10211]
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.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
Solve \begin {gather*} \boxed {y^{2} \left (\left (y^{\prime }\right )^{2}+1\right )-a^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 59
dsolve(y(x)^2*(1+diff(y(x),x)^2)=a^2,y(x), singsol=all)
\begin{align*} y \relax (x ) = -a \\ y \relax (x ) = a \\ y \relax (x ) = \sqrt {a^{2}-x^{2}+2 x c_{1}-c_{1}^{2}} \\ y \relax (x ) = -\sqrt {a^{2}-x^{2}+2 x c_{1}-c_{1}^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.226 (sec). Leaf size: 101
DSolve[y[x]^2*(1+(y'[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*}