74.3.18 problem 14 (c)

Internal problem ID [15807]
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 : Monday, March 31, 2025 at 01:54:10 PM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (3\right )&=-6 \end{align*}

✓ Maple. Time used: 0.078 (sec). Leaf size: 14

ode:=diff(y(t),t) = (25-y(t)^2)^(1/2); 
ic:=y(3) = -6; 
dsolve([ode,ic],y(t), singsol=all);
 

\[ y = 5 \sin \left (t -3-\arcsin \left (\frac {6}{5}\right )\right ) \]

✓ Mathematica. Time used: 0.042 (sec). Leaf size: 49

ode=D[y[t],t]==Sqrt[25-y[t]^2]; 
ic={y[3]==-6}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\[ y(t)\to \frac {5 \tan \left (-i \text {arctanh}\left (\frac {6}{\sqrt {11}}\right )-t+3\right )}{\sqrt {\sec ^2\left (-i \text {arctanh}\left (\frac {6}{\sqrt {11}}\right )-t+3\right )}} \]

✗ Sympy

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-sqrt(25 - y(t)**2) + Derivative(y(t), t),0) 
ics = {y(3): -6} 
dsolve(ode,func=y(t),ics=ics)
 

NotImplementedError : Initial conditions produced too many solutions for constants