76.5.1 problem 1

Internal problem ID [17421]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.7 (Substitution Methods). Problems at page 108
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 10:06:42 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 29

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

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

✓ Solution by Mathematica

Time used: 0.091 (sec). Leaf size: 41

DSolve[y[x]*D[y[x],x]==x+1,y[x],x,IncludeSingularSolutions -> True]
 

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