76.3.8 problem 8

Internal problem ID [17308]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.4 (Differences between linear and nonlinear equations). Problems at page 79
Problem number : 8
Date solved : Monday, March 31, 2025 at 03:51:44 PM
CAS classification : [`y=_G(x,y')`]

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

✗ Maple

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

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : The given ODE -sqrt(-t**2 - y(t)**2 + 1) + Derivative(y(t), t) cannot be solved by the lie group method