85.12.2 problem 2

Internal problem ID [22496]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 40
Problem number : 2
Date solved : Thursday, October 02, 2025 at 08:42:48 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

With initial conditions

\begin{align*} y \left (1\right )&=1 \\ \end{align*}

✓ Maple. Time used: 0.014 (sec). Leaf size: 13

ode:=diff(y(x),x) = y(x)/x+y(x)^2/x^2; 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.092 (sec). Leaf size: 21

ode=D[y[x],x]== y[x]/x+y[x]^2/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: 0.114 (sec). Leaf size: 8

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

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