8.2.13 problem 17

Internal problem ID [673]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.3. Slope fields and solution curves. Page 26
Problem number : 17
Date solved : Monday, January 27, 2025 at 02:57:12 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: 0.019 (sec). Leaf size: 9

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

\[ y = 1-x \]

✓ Solution by Mathematica

Time used: 0.091 (sec). Leaf size: 14

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

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