Internal problem ID [1876]
Book: Differential Equations, Nelson, Folley, Coral, 3rd ed, 1964
Section: Exercis 5, page 21
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\sqrt {1-x^{2}}+\sqrt {1-y^{2}}\, y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.003 (sec). Leaf size: 34
dsolve(sqrt(1-x^2)+sqrt(1-y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ c_{1}+x \sqrt {-x^{2}+1}+\arcsin \relax (x )+y \relax (x ) \sqrt {1-y \relax (x )^{2}}+\arcsin \left (y \relax (x )\right ) = 0 \]
✓ Solution by Mathematica
Time used: 0.606 (sec). Leaf size: 83
DSolve[Sqrt[1-x^2]+Sqrt[1-y[x]^2]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}\left [\frac {1}{2} \text {$\#$1} \sqrt {1-\text {$\#$1}^2}-\text {ArcTan}\left (\frac {\sqrt {1-\text {$\#$1}^2}}{\text {$\#$1}+1}\right )\&\right ]\left [-\frac {1}{2} \sqrt {1-x^2} x+\cot ^{-1}\left (\frac {x+1}{\sqrt {1-x^2}}\right )+c_1\right ] \\ \end{align*}