Internal problem ID [10157]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter 2, differential equations of the first order and the first degree. Article 19. Summary.
Page 29
Problem number: Ex 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {x \sqrt {1-y^{2}}+y \sqrt {-x^{2}+1}\, y^{\prime }=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 40
dsolve(x*sqrt(1-y(x)^2)+y(x)*sqrt(1-x^2)*diff(y(x),x)=0,y(x), singsol=all)
\[ \frac {\left (x -1\right ) \left (1+x \right )}{\sqrt {-x^{2}+1}}+\frac {\left (y \relax (x )-1\right ) \left (y \relax (x )+1\right )}{\sqrt {1-y \relax (x )^{2}}}+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 3.807 (sec). Leaf size: 77
DSolve[x*Sqrt[1-y[x]^2]+y[x]*Sqrt[1-x^2]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sqrt {x^2-c_1 \left (2 \sqrt {1-x^2}+c_1\right )} \\ y(x)\to \sqrt {x^2-c_1 \left (2 \sqrt {1-x^2}+c_1\right )} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}