8.5.9 problem 9

Internal problem ID [737]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 1.6, Substitution methods and exact equations. Page 74
Problem number : 9
Date solved : Saturday, March 29, 2025 at 10:17:17 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

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

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

✓ Mathematica. Time used: 0.124 (sec). Leaf size: 21

ode=x^2*D[y[x],x] == x*y[x]+y[x]^2; 
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: 0.192 (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)
 

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