76.4.10 problem 10

Internal problem ID [17333]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.6 (Exact equations and integrating factors). Problems at page 100
Problem number : 10
Date solved : Monday, March 31, 2025 at 03:54:33 PM
CAS classification : [_linear]

\begin{align*} \frac {y}{x}+6 x +\left (\ln \left (x \right )-2\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 18

ode:=y(x)/x+6*x+(ln(x)-2)*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {-3 x^{2}+c_1}{\ln \left (x \right )-2} \]

✓ Mathematica. Time used: 0.085 (sec). Leaf size: 20

ode=(y[x]/x+6*x)+(Log[x]-2)*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {-3 x^2+c_1}{\log (x)-2} \]

✓ Sympy. Time used: 0.313 (sec). Leaf size: 14

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(6*x + (log(x) - 2)*Derivative(y(x), x) + y(x)/x,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {C_{1} - 3 x^{2}}{\log {\left (x \right )} - 2} \]