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 : Friday, February 07, 2025 at 08:11:45 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*}

✓ Solution by Maple

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

dsolve([diff(y(x),x)=1/sqrt(x+2),y(2) = -1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

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

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

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