38.2.28 problem 28

Internal problem ID [8246]
Book : A First Course in Differential Equations with Modeling Applications by Dennis G. Zill. 12 ed. Metric version. 2024. Cengage learning.
Section : Chapter 1. Introduction to differential equations. Section 1.2 Initial value problems. Exercises 1.2 at page 19
Problem number : 28
Date solved : Tuesday, September 30, 2025 at 05:20:11 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\sqrt {y^{2}-9} \end{align*}

With initial conditions

\begin{align*} y \left (-1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.455 (sec). Leaf size: 18

ode:=diff(y(x),x) = (y(x)^2-9)^(1/2); 
ic:=[y(-1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \cosh \left (1+x \right )+2 i \sqrt {2}\, \sinh \left (1+x \right ) \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 46

ode=D[y[x],x]==Sqrt[y[x]^2-9]; 
ic={y[-1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} e^{-x-1} \left (\left (1+2 i \sqrt {2}\right ) e^{2 x+2}+1-2 i \sqrt {2}\right ) \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sqrt(y(x)**2 - 9) + Derivative(y(x), x),0) 
ics = {y(-1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : Initial conditions produced too many solutions for constants