Internal problem ID [14983]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 4. Equations with variables separable and equations reducible to them. Exercises
page 38
Problem number: 56.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {2 x \sqrt {1-y^{2}}-\left (x^{2}+1\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 15
dsolve(2*x*sqrt(1-y(x)^2)=diff(y(x),x)*(1+x^2),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (\ln \left (x^{2}+1\right )+2 c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.271 (sec). Leaf size: 33
DSolve[2*x*Sqrt[1-y[x]^2]==y'[x]*(1+x^2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \cos \left (\log \left (x^2+1\right )+c_1\right ) \\ y(x)\to -1 \\ y(x)\to 1 \\ y(x)\to \text {Interval}[\{-1,1\}] \\ \end{align*}