8.1.5 problem 5

Internal problem ID [655]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.2. Integrals as general and particular solutions. Page 16
Problem number : 5
Date solved : Monday, January 27, 2025 at 02:56:45 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/(2+x)^(1/2),y(2) = -1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 16

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

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