8.2.14 problem 18

Internal problem ID [674]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.3. Slope fields and solution curves. Page 26
Problem number : 18
Date solved : Monday, January 27, 2025 at 02:57:14 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: 0.003 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.042 (sec). Leaf size: 29

DSolve[{y[x]*D[y[x],x] == -1+x,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*}