29.14.9 problem 390

Internal problem ID [4988]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 14
Problem number : 390
Date solved : Tuesday, March 04, 2025 at 07:40:27 PM
CAS classification : [_separable]

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 9

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

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

✓ Mathematica. Time used: 0.328 (sec). Leaf size: 25

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

\begin{align*} y(x)\to \tan (\arcsin (x)+c_1) \\ y(x)\to -i \\ y(x)\to i \\ \end{align*}

✓ Sympy. Time used: 0.696 (sec). Leaf size: 8

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

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