71.6.11 problem 11

Internal problem ID [14417]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 2. The Initial Value Problem. Exercises 2.3.2, page 63
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 06:30:18 AM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 19

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

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

✓ Solution by Mathematica

Time used: 0.011 (sec). Leaf size: 31

DSolve[2*y[x]*D[y[x],x]==1,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*}