44.1.21 problem 2(g)

Internal problem ID [9079]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.2 THE NATURE OF SOLUTIONS. Page 9
Problem number : 2(g)
Date solved : Tuesday, September 30, 2025 at 06:03:48 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\arcsin \left (x \right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 19

ode:=diff(y(x),x) = arcsin(x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.003 (sec). Leaf size: 23

ode=D[y[x],x]==ArcSin[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x \arcsin (x)+\sqrt {1-x^2}+c_1 \end{align*}

✓ Sympy. Time used: 0.054 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = C_{1} + x \operatorname {asin}{\left (x \right )} + \sqrt {1 - x^{2}} \]