44.2.25 problem 25

Internal problem ID [6957]
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 : 25
Date solved : Wednesday, March 05, 2025 at 03:56:41 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (1\right )&=4 \end{align*}

✓ Maple. Time used: 0.227 (sec). Leaf size: 33

ode:=diff(y(x),x) = (y(x)^2-9)^(1/2); 
ic:=y(1) = 4; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -\frac {\left (\left (-4-\sqrt {7}\right ) {\mathrm e}^{2 x}+{\mathrm e}^{2} \left (\sqrt {7}-4\right )\right ) {\mathrm e}^{-x -1}}{2} \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 40

ode=D[y[x],x]==Sqrt[y[x]^2-9]; 
ic={y[1]==4}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{2} \left (4+\sqrt {7}\right ) e^{x-1}-\frac {1}{2} \left (\sqrt {7}-4\right ) e^{1-x} \]

✗ 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): 4} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : Initial conditions produced too many solutions for constants