62.12.2 problem Ex 2

Internal problem ID [12848]
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 2
Date solved : Tuesday, January 28, 2025 at 04:26:57 AM
CAS classification : [_separable]

\begin{align*} \sqrt {1-y^{2}}+\sqrt {-x^{2}+1}\, y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 11

dsolve(sqrt(1-y(x)^2)+sqrt(1-x^2)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = -\sin \left (\arcsin \left (x \right )+c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.202 (sec). Leaf size: 33

DSolve[Sqrt[1-y[x]^2]+Sqrt[1-x^2]*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sin (\arcsin (x)-c_1) \\ y(x)\to -1 \\ y(x)\to 1 \\ y(x)\to \text {Interval}[\{-1,1\}] \\ \end{align*}