30.5.9 problem 9

Internal problem ID [7508]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.6, Substitutions and Transformations. Exercises. page 76
Problem number : 9
Date solved : Tuesday, September 30, 2025 at 04:40:41 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

\[ y = \frac {x}{-\ln \left (x \right )+c_1} \]

✓ Mathematica. Time used: 0.083 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.112 (sec). Leaf size: 8

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

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