29.4.7 problem 7

Internal problem ID [7260]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 4. OTHER METHODS FOR FIRST-ORDER EQUATIONS. page 406
Problem number : 7
Date solved : Tuesday, September 30, 2025 at 04:27:14 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.085 (sec). Leaf size: 19

ode=x^2*D[y[x],x]+(y[x]^2-x*y[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: 0.111 (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)
 

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