Internal problem ID [935]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number: 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\left (x -1\right ) \left (y-1\right ) \left (y-2\right )=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 35
dsolve(diff(y(x),x)=(x-1)*(y(x)-1)*(y(x)-2),y(x), singsol=all)
\[ y \left (x \right ) = \frac {-2+c_{1} {\mathrm e}^{\frac {1}{2} x^{2}-x}}{c_{1} {\mathrm e}^{\frac {1}{2} x^{2}-x}-1} \]
✓ Solution by Mathematica
Time used: 0.308 (sec). Leaf size: 56
DSolve[y'[x]==(x-1)*(y[x]-1)*(y[x]-2),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {2 e^x-e^{\frac {x^2}{2}+c_1}}{e^x-e^{\frac {x^2}{2}+c_1}} y(x)\to 1 y(x)\to 2 \end{align*}