44.2.26 problem 26

Internal problem ID [6958]
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 : 26
Date solved : Wednesday, March 05, 2025 at 03:59:30 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} y \left (5\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(5) = 3; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 3 \]

✓ Mathematica. Time used: 0.002 (sec). Leaf size: 6

ode=D[y[x],x]==Sqrt[y[x]^2-9]; 
ic={y[5]==3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 3 \]

✓ Sympy. Time used: 0.823 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-sqrt(y(x)**2 - 9) + Derivative(y(x), x),0) 
ics = {y(5): 3} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {3 e^{5 - x}}{2} + \frac {3 e^{x - 5}}{2} \]