19.1.9 problem 9

Internal problem ID [3523]
Book : Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section : 1.4, page 36
Problem number : 9
Date solved : Monday, January 27, 2025 at 07:40:28 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: 0.006 (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: 0.823 (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*}