20.2.9 problem Problem 9

Internal problem ID [3601]
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
Date solved : Monday, January 27, 2025 at 07:47:13 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 21

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

\[ y \left (x \right ) = -\tanh \left (-\frac {\ln \left (x -1\right )}{2}+\ln \left (x -2\right )+\frac {c_{1}}{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.776 (sec). Leaf size: 51

DSolve[D[y[x],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*}