68.3.19 problem 14 (c)

Internal problem ID [17166]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number : 14 (c)
Date solved : Friday, October 03, 2025 at 12:40:48 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\sqrt {25-y^{2}} \end{align*}

With initial conditions

\begin{align*} y \left (4\right )&=-5 \\ \end{align*}

✓ Maple. Time used: 0.010 (sec). Leaf size: 5

ode:=diff(y(t),t) = (25-y(t)^2)^(1/2); 
ic:=[y(4) = -5]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = -5 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 6

ode=D[y[t],t]==Sqrt[25-y[t]^2]; 
ic={y[4]==-5}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -5 \end{align*}

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-sqrt(25 - y(t)**2) + Derivative(y(t), t),0) 
ics = {y(4): -5} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : Initial conditions produced too many solutions for constants