Internal problem ID [2553]
Book: Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section: Chapter 11.3, page 316
Problem number: 11.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } x^{2}-y^{2}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = -1] \end {align*}
✓ Solution by Maple
Time used: 0.034 (sec). Leaf size: 14
dsolve([x^2*diff(y(x),x)-y(x)^2=0,y(1) = -1],y(x), singsol=all)
\[ y \relax (x ) = -\frac {x}{2 x -1} \]
✓ Solution by Mathematica
Time used: 0.109 (sec). Leaf size: 14
DSolve[{x^2*y'[x]-y[x]^2==0,y[1]==-1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{1-2 x} \\ \end{align*}