78.1.23 problem 13

Internal problem ID [20949]
Book : A FIRST COURSE IN DIFFERENTIAL EQUATIONS FOR SCIENTISTS AND ENGINEERS. By Russell Herman. University of North Carolina Wilmington. LibreText. compiled on 06/09/2025
Section : Chapter 1, First order ODEs. Problems section 1.5
Problem number : 13
Date solved : Thursday, October 02, 2025 at 07:00:20 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Bernoulli]

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

With initial conditions

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

✓ Maple. Time used: 0.047 (sec). Leaf size: 13

ode:=diff(y(x),x) = (y(x)^2+x*y(x))/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: 0.088 (sec). Leaf size: 14

ode=D[y[x],x]==(y[x]^2+x*y[x])/x^2; 
ic={y[1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {x}{\log (x)-1} \end{align*}

✓ Sympy. Time used: 0.124 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (x*y(x) + y(x)**2)/x**2,0) 
ics = {y(1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

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