30.5.16 problem 16

Internal problem ID [7515]
Book : Fundamentals of Differential Equations. By Nagle, Saff and Snider. 9th edition. Boston. Pearson 2018.
Section : Chapter 2, First order differential equations. Section 2.6, Substitutions and Transformations. Exercises. page 76
Problem number : 16
Date solved : Tuesday, September 30, 2025 at 04:41:37 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y^{\prime }&=\frac {y \left (\ln \left (y\right )-\ln \left (x \right )+1\right )}{x} \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 10

ode:=diff(y(x),x) = y(x)*(ln(y(x))-ln(x)+1)/x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x \,{\mathrm e}^{c_1 x} \]

✓ Mathematica. Time used: 0.139 (sec). Leaf size: 20

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

\begin{align*} y(x)&\to x e^{e^{c_1} x}\\ y(x)&\to x \end{align*}

✓ Sympy. Time used: 0.334 (sec). Leaf size: 8

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

\[ y{\left (x \right )} = x e^{C_{1} x} \]