71.1.6 problem 20

Internal problem ID [14315]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 1. Introduction. Exercises page 14
Problem number : 20
Date solved : Tuesday, January 28, 2025 at 06:26:23 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }+\frac {1}{2 y}&=0 \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

dsolve(diff(y(x),x)+1/(2*y(x))=0,y(x), singsol=all)
 

\begin{align*} y &= \sqrt {-x +c_{1}} \\ y &= -\sqrt {-x +c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.068 (sec). Leaf size: 35

DSolve[D[y[x],x]+1/(2*y[x])==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {-x+2 c_1} \\ y(x)\to \sqrt {-x+2 c_1} \\ \end{align*}