Internal problem ID [2121]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 1, First-Order Differential Equations. Section 1.4, Separable Differential Equations.
page 43
Problem number: Problem 9.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {x \left (-1+y^{2}\right )}{2 \left (-2+x \right ) \left (x -1\right )}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve(diff(y(x),x)=x*(y(x)^2-1)/(2*(x-2)*(x-1)),y(x), singsol=all)
\[ y \relax (x ) = -\tanh \left (\ln \left (-2+x \right )-\frac {\ln \left (x -1\right )}{2}+\frac {c_{1}}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.846 (sec). Leaf size: 51
DSolve[y'[x]==x*(y[x]^2-1)/(2*(x-2)*(x-1)),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {x+e^{2 c_1} (x-2)^2-1}{-x+e^{2 c_1} (x-2)^2+1} \\ y(x)\to -1 \\ y(x)\to 1 \\ \end{align*}