25.1.11 problem 11

Internal problem ID [4223]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 11
Date solved : Monday, January 27, 2025 at 08:42:52 AM
CAS classification : [_separable]

\begin{align*} x^{2} y^{\prime }-y^{2}&=0 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 14

dsolve([x^2*diff(y(x),x)-y(x)^2=0,y(1) = -1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.121 (sec). Leaf size: 14

DSolve[{x^2*D[y[x],x]-y[x]^2==0,y[1]==-1},y[x],x,IncludeSingularSolutions -> True]
 

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