68.3.16 problem 14 (a)

Internal problem ID [17163]
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 (a)
Date solved : Thursday, October 02, 2025 at 01:45:46 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (-4\right )&=3 \\ \end{align*}

✓ Maple. Time used: 0.061 (sec). Leaf size: 12

ode:=diff(y(t),t) = (25-y(t)^2)^(1/2); 
ic:=[y(-4) = 3]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = 5 \sin \left (t +4+\arcsin \left (\frac {3}{5}\right )\right ) \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 29

ode=D[y[t],t]==Sqrt[25-y[t]^2]; 
ic={y[-4]==3}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to \frac {5 \tan \left (\arctan \left (\frac {3}{4}\right )+t+4\right )}{\sqrt {\sec ^2\left (\arctan \left (\frac {3}{4}\right )+t+4\right )}} \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): 3} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : Initial conditions produced too many solutions for constants