Internal problem ID [12125]
Book: Differential equations and the calculus of variations by L. ElSGOLTS. MIR PUBLISHERS,
MOSCOW, Third printing 1977.
Section: Chapter 1, First-Order Differential Equations. Problems page 88
Problem number: Problem 14.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [_quadrature]
\[ \boxed {{y^{\prime }}^{2}=-x^{2}+1} \]
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 43
dsolve(x^2+diff(y(x),x)^2=1,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {x \sqrt {-x^{2}+1}}{2}+\frac {\arcsin \left (x \right )}{2}+c_{1} \\ y \left (x \right ) &= -\frac {x \sqrt {-x^{2}+1}}{2}-\frac {\arcsin \left (x \right )}{2}+c_{1} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.07 (sec). Leaf size: 85
DSolve[x^2+y'[x]^2==1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\arctan \left (\frac {\sqrt {1-x^2}}{x+1}\right )+\frac {1}{2} \sqrt {1-x^2} x+c_1 \\ y(x)\to \arctan \left (\frac {\sqrt {1-x^2}}{x+1}\right )-\frac {1}{2} \sqrt {1-x^2} x+c_1 \\ \end{align*}