Internal problem ID [11652]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number: 15.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {y}{x}+\frac {y^{2}}{x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 11
dsolve(diff(y(x),x)-y(x)/x=-y(x)^2/x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x}{c_{1} +x} \]
✓ Solution by Mathematica
Time used: 0.238 (sec). Leaf size: 25
DSolve[y'[x]-y[x]/x==-y[x]^2/x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {x}{x+e^{c_1}} \\ y(x)\to 0 \\ y(x)\to 1 \\ \end{align*}