7.1.5 problem 5

Internal problem ID [5]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 1. First order differential equations. Section 1.2. Problems at page 17
Problem number : 5
Date solved : Tuesday, March 04, 2025 at 10:37:58 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {1}{\sqrt {x +2}} \end{align*}

With initial conditions

\begin{align*} y \left (2\right )&=-1 \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 13

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

\[ y = 2 \sqrt {x +2}-5 \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 16

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

\[ y(x)\to 2 \sqrt {x+2}-5 \]

✓ Sympy. Time used: 0.142 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = 2 \sqrt {x + 2} - 5 \]