75.2.5 problem 25

Internal problem ID [16682]
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
Date solved : Tuesday, January 28, 2025 at 09:17:53 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\left (y-1\right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 14

dsolve(diff(y(x),x)=(y(x)-1)^2,y(x), singsol=all)
 

\[ y = \frac {x -1+c_{1}}{x +c_{1}} \]

✓ Solution by Mathematica

Time used: 0.109 (sec). Leaf size: 22

DSolve[D[y[x],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*}