14.3.8 problem Problem 8

Internal problem ID [3617]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.6, First-Order Linear Differential Equations. page 59
Problem number : Problem 8
Date solved : Tuesday, September 30, 2025 at 06:48:34 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {y}{x \ln \left (x \right )}&=9 x^{2} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 23

ode:=diff(y(x),x)+y(x)/x/ln(x) = 9*x^2; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 25

ode=D[y[x],x]+1/(x*Log[x])*y[x]==9*x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {-x^3+3 x^3 \log (x)+c_1}{\log (x)} \end{align*}

✓ Sympy. Time used: 0.167 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-9*x**2 + Derivative(y(x), x) + y(x)/(x*log(x)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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