80.1.5 problem 6

Internal problem ID [18464]
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 : Monday, March 31, 2025 at 05:30:02 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 8

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

\[ y = \sin \left (c_1 x \right ) \]

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

ode=D[y[x],x]==1/x*Sqrt[1-y[x]^2]*ArcSin[y[x]]; 
ic={}; 
DSolve[{ode,ic},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*}

✓ Sympy. Time used: 0.288 (sec). Leaf size: 7

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - sqrt(1 - y(x)**2)*asin(y(x))/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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