15.7.8 problem 8

Internal problem ID [2989]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 11, page 45
Problem number : 8
Date solved : Tuesday, March 04, 2025 at 03:38:28 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 12

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

\[ y = \frac {x}{\ln \left (x \right )+c_{1}} \]

✓ Mathematica. Time used: 0.155 (sec). Leaf size: 19

ode=x^2*D[y[x],x]+y[x]^2==x*y[x]; 
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: 0.289 (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)
 

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