Internal problem ID [14952]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 2. The method of isoclines. Exercises page 27
Problem number: 25.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }-\left (y-1\right )^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(y(x),x)=(y(x)-1)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} +x -1}{c_{1} +x} \]
✓ Solution by Mathematica
Time used: 0.107 (sec). Leaf size: 22
DSolve[y'[x]==(y[x]-1)^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x-1+c_1}{x+c_1} \\ y(x)\to 1 \\ \end{align*}