Internal problem ID [14978]
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: 51.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 5
dsolve([x*sqrt(1-y(x)^2)+y(x)*sqrt(1-x^2)*diff(y(x),x)=0,y(0) = 1],y(x), singsol=all)
\[ y \left (x \right ) = 1 \]
✓ Solution by Mathematica
Time used: 3.582 (sec). Leaf size: 32
DSolve[{x*Sqrt[1-y[x]^2]+y[x]*Sqrt[1-x^2]*y'[x]==0,{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 1 \\ y(x)\to \sqrt {x^2+2 \sqrt {1-x^2}-1} \\ \end{align*}