44.2.27 problem 27

Internal problem ID [6959]
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 : 27
Date solved : Wednesday, March 05, 2025 at 03:59:34 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (2\right )&=-3 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 5

ode:=diff(y(x),x) = (y(x)^2-9)^(1/2); 
ic:=y(2) = -3; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = -3 \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 25

ode=D[y[x],x]==Sqrt[y[x]^2-9]; 
ic={y[2]==-3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {3}{2} e^{-x-2} \left (e^{2 x}+e^4\right ) \]

✓ Sympy. Time used: 0.828 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sqrt(y(x)**2 - 9) + Derivative(y(x), x),0) 
ics = {y(2): -3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {3 e^{2 - x}}{2} - \frac {3 e^{x - 2}}{2} \]