78.1.18 problem 2 (d)

Internal problem ID [18002]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 1. The Nature of Differential Equations. Separable Equations. Section 2. Problems at page 9
Problem number : 2 (d)
Date solved : Monday, March 31, 2025 at 04:56:09 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.001 (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: 0.004 (sec). Leaf size: 23

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

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

✓ Sympy. Time used: 0.083 (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)
 

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