25.1.19 problem 19

Internal problem ID [4231]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 19
Date solved : Monday, January 27, 2025 at 08:43:13 AM
CAS classification : [_separable]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.038 (sec). Leaf size: 15

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

\[ y \left (x \right ) = -\frac {1}{2 x^{2}-1} \]

✓ Solution by Mathematica

Time used: 0.316 (sec). Leaf size: 14

DSolve[{x*D[y[x],x]==2*y[x]*(y[x]-1),y[1/2]==2},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{1-2 x^2} \]