68.3.17 problem 14 (b)

Internal problem ID [17164]
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 (b)
Date solved : Thursday, October 02, 2025 at 01:47:46 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (0\right )&=5 \\ \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 5

ode:=diff(y(t),t) = (25-y(t)^2)^(1/2); 
ic:=[y(0) = 5]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = 5 \]

✓ Mathematica. Time used: 0.001 (sec). Leaf size: 6

ode=D[y[t],t]==Sqrt[25-y[t]^2]; 
ic={y[0]==5}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.165 (sec). Leaf size: 7

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

\[ y{\left (t \right )} = 5 \cos {\left (t \right )} \]