Internal problem ID [3070]
Book: Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section: Chapter 11.3, page 316
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {x y^{\prime }-2 y \left (y-1\right )=0} \] With initial conditions \begin {align*} \left [y \left (\frac {1}{2}\right ) = 2\right ] \end {align*}
✓ Solution by Maple
Time used: 0.047 (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: 0.339 (sec). Leaf size: 14
DSolve[{x*y'[x]==2*y[x]*(y[x]-1),y[1/2]==2},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{1-2 x^2} \]