Internal problem ID [6175]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven
Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 1. What is a differential equation. Section 1.4 First Order Linear Equations.
Page 15
Problem number: 3(c).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class G`], _rational, _Bernoulli]
\[ \boxed {x y^{\prime }+y-x y^{2}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 16
dsolve(x*diff(y(x),x)+y(x)=x*y(x)^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {1}{\left (-\ln \left (x \right )+c_{1} \right ) x} \]
✓ Solution by Mathematica
Time used: 0.128 (sec). Leaf size: 22
DSolve[x*y'[x]+y[x]==x*y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{-x \log (x)+c_1 x} \\ y(x)\to 0 \\ \end{align*}