68.1.53 problem 73

Internal problem ID [17120]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 73
Date solved : Thursday, October 02, 2025 at 01:43:30 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

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

ode:=diff(y(x),x) = (y(x)^2+2*x*y(x))/x^2; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.09 (sec). Leaf size: 23

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

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

✓ Sympy. Time used: 0.115 (sec). Leaf size: 8

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

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