15.1.7 problem 7

Internal problem ID [2847]
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
Date solved : Monday, January 27, 2025 at 06:19:47 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 34

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

\[ c_1 +x \sqrt {-x^{2}+1}+\arcsin \left (x \right )+y \sqrt {1-y^{2}}+\arcsin \left (y\right ) = 0 \]

✓ Solution by Mathematica

Time used: 0.525 (sec). Leaf size: 55

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

\[ y(x)\to \text {InverseFunction}\left [\frac {1}{2} \left (\text {$\#$1} \sqrt {1-\text {$\#$1}^2}+\arcsin (\text {$\#$1})\right )\&\right ]\left [-\frac {\arcsin (x)}{2}-\frac {1}{2} \sqrt {1-x^2} x+c_1\right ] \]