Internal problem ID [3932]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 2. Special types of differential equations of the first kind. Lesson 7
Problem number: First order with homogeneous Coefficients. Exercise 7.15, page
61.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, class A], _rational, _Bernoulli]
Solve \begin {gather*} \boxed {x y-y^{2}-x^{2} y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} [y \relax (1) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 12
dsolve([(x*y(x)-y(x)^2)-x^2*diff(y(x),x)=0,y(1) = 1],y(x), singsol=all)
\[ y \relax (x ) = \frac {x}{\ln \relax (x )+1} \]
✓ Solution by Mathematica
Time used: 0.161 (sec). Leaf size: 13
DSolve[{(x*y[x]-y[x]^2)-x^2*y'[x]==0,y[1]==1},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{\log (x)+1} \\ \end{align*}