7.2.16 problem 18

Internal problem ID [34]
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 1.3. Problems at page 27
Problem number : 18
Date solved : Friday, February 07, 2025 at 08:12:29 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.015 (sec). Leaf size: 15

dsolve([y(x)*diff(y(x),x)=x-1,y(1) = 0],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 29

DSolve[{y[x]*D[y[x],x]==x-1,{y[1]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\sqrt {(x-1)^2} \\ y(x)\to \sqrt {(x-1)^2} \\ \end{align*}