32.5.17 problem Exercise 11.18, page 97

Internal problem ID [5855]
Book : Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section : Chapter 2. Special types of differential equations of the first kind. Lesson 11, Bernoulli Equations
Problem number : Exercise 11.18, page 97
Date solved : Monday, January 27, 2025 at 01:20:54 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

dsolve(x*diff(y(x),x)+x*y(x)^2-y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {2 x}{x^{2}+2 c_{1}} \]

✓ Solution by Mathematica

Time used: 0.154 (sec). Leaf size: 23

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

\begin{align*} y(x)\to \frac {2 x}{x^2+2 c_1} \\ y(x)\to 0 \\ \end{align*}