7.2.15 problem 17

Internal problem ID [33]
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 : 17
Date solved : Friday, February 07, 2025 at 08:12:23 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.027 (sec). Leaf size: 9

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

\[ y = 1-x \]

✓ Solution by Mathematica

Time used: 0.095 (sec). Leaf size: 14

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

\[ y(x)\to \sqrt {(x-1)^2} \]