89.4.1 problem 1

Internal problem ID [24323]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 39
Problem number : 1
Date solved : Thursday, October 02, 2025 at 10:18:03 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} y \left (1+2 y x \right )-x y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

ode:=y(x)*(2*x*y(x)+1)-x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {x}{-x^{2}+c_1} \]

✓ Mathematica. Time used: 0.086 (sec). Leaf size: 23

ode=y[x]*( 2*x*y[x]+1 )-x *D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.108 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*Derivative(y(x), x) + (2*x*y(x) + 1)*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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