Internal problem ID [12435]
Book: DIFFERENTIAL and INTEGRAL CALCULUS. VOL I. by N. PISKUNOV. MIR
PUBLISHERS, Moscow 1969.
Section: Chapter 8. Differential equations. Exercises page 595
Problem number: 21.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime }-\sqrt {1-y^{2}}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 9
dsolve((1+x^2)*diff(y(x),x)-sqrt(1-y(x)^2)=0,y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (\arctan \left (x \right )+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.479 (sec). Leaf size: 29
DSolve[(1+x^2)*y'[x]-Sqrt[1-y[x]^2]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \cos (\arctan (x)+c_1) \\ y(x)\to -1 \\ y(x)\to 1 \\ y(x)\to \text {Interval}[\{-1,1\}] \\ \end{align*}