80.1.5 problem 6

Internal problem ID [18535]
Book : Elementary Differential Equations. By Thornton C. Fry. D Van Nostrand. NY. First Edition (1929)
Section : Chapter 1. section 5. Problems at page 19
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 11:54:28 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {\sqrt {1-y^{2}}\, \arcsin \left (y\right )}{x} \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 8

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

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

✓ Solution by Mathematica

Time used: 0.333 (sec). Leaf size: 27

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

\begin{align*} y(x)\to \sin \left (e^{c_1} x\right ) \\ y(x)\to -1 \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}