Internal problem ID [24]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y y^{\prime }=x -1} \] With initial conditions \begin {align*} [y \left (1\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 15
dsolve([y(x)*diff(y(x),x) = -1+x,y(1) = 0],y(x), singsol=all)
\begin{align*} y \left (x \right ) = 1-x y \left (x \right ) = x -1 \end{align*}
✓ Solution by Mathematica
Time used: 0.052 (sec). Leaf size: 29
DSolve[{y[x]*y'[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*}