16.1.3 problem 2(c)

Internal problem ID [3405]
Book : Elementary Differential Equations, Martin, Reissner, 2nd ed, 1961
Section : Exercis 2, page 5
Problem number : 2(c)
Date solved : Tuesday, March 04, 2025 at 04:37:47 PM
CAS classification : [_quadrature]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 10

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

\[ y \left (x \right ) = 2 \arcsin \left (x \right )+c_{1} \]

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 12

ode=D[y[x],x]==2/Sqrt[1-x^2]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 2 \arcsin (x)+c_1 \]

✓ Sympy. Time used: 0.153 (sec). Leaf size: 8

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

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