Internal problem ID [3843]
Book: Differential and integral calculus, vol II By N. Piskunov. 1974
Section: Chapter 1
Problem number: example page 46.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{2} \left (1+{y^{\prime }}^{2}\right )-R^{2}=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 59
dsolve(y(x)^2*(1+diff(y(x),x)^2)=R^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) = -R \\ y \left (x \right ) = R \\ y \left (x \right ) = \sqrt {R^{2}-c_{1}^{2}+2 c_{1} x -x^{2}} \\ y \left (x \right ) = -\sqrt {R^{2}-c_{1}^{2}+2 c_{1} x -x^{2}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.221 (sec). Leaf size: 101
DSolve[y[x]^2*(1+(y'[x])^2)==R^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {R^2-(x+c_1){}^2} \\ y(x)\to \sqrt {R^2-(x+c_1){}^2} \\ y(x)\to -\sqrt {R^2-(x-c_1){}^2} \\ y(x)\to \sqrt {R^2-(x-c_1){}^2} \\ y(x)\to -R \\ y(x)\to R \\ \end{align*}