Internal problem ID [1876]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 5, page 21
Problem number: 7.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\sqrt {1-y^{2}}\, y^{\prime }=-\sqrt {1-x^{2}}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(sqrt(1-x^2)+sqrt(1-y(x)^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ c_{1} +x \sqrt {-x^{2}+1}+\arcsin \left (x \right )+y \left (x \right ) \sqrt {1-y \left (x \right )^{2}}+\arcsin \left (y \left (x \right )\right ) = 0 \]
✓ Solution by Mathematica
Time used: 0.626 (sec). Leaf size: 85
DSolve[Sqrt[1-x^2]+Sqrt[1-y[x]^2]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \text {InverseFunction}\left [\frac {1}{2} \text {$\#$1} \sqrt {1-\text {$\#$1}^2}-\arctan \left (\frac {\sqrt {1-\text {$\#$1}^2}}{\text {$\#$1}+1}\right )\&\right ]\left [\arctan \left (\frac {\sqrt {1-x^2}}{x+1}\right )-\frac {1}{2} \sqrt {1-x^2} x+c_1\right ] \]