Internal problem ID [23]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y y^{\prime }-x +1=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 9
dsolve([y(x)*diff(y(x),x) = -1+x,y(0) = 1],y(x), singsol=all)
\[ y \relax (x ) = 1-x \]
✓ Solution by Mathematica
Time used: 0.079 (sec). Leaf size: 14
DSolve[{y[x]*y'[x] == -1+x,y[0]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \sqrt {(x-1)^2} \\ \end{align*}