29.26.20 problem 756

Internal problem ID [5341]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 26
Problem number : 756
Date solved : Tuesday, March 04, 2025 at 09:29:47 PM
CAS classification : [_quadrature]

\begin{align*} {y^{\prime }}^{2}&=1-y^{2} \end{align*}

✓ Maple. Time used: 0.033 (sec). Leaf size: 29

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

\begin{align*} y \left (x \right ) &= -1 \\ y \left (x \right ) &= 1 \\ y \left (x \right ) &= -\sin \left (-x +c_{1} \right ) \\ y \left (x \right ) &= \sin \left (-x +c_{1} \right ) \\ \end{align*}

✓ Mathematica. Time used: 0.086 (sec). Leaf size: 41

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

\begin{align*} y(x)\to -\sin (x-c_1) \\ y(x)\to \sin (x+c_1) \\ y(x)\to -1 \\ y(x)\to 1 \\ y(x)\to \text {Interval}[\{-1,1\}] \\ \end{align*}

✓ Sympy. Time used: 154.830 (sec). Leaf size: 14

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

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