78.6.9 problem 2 (i)

Internal problem ID [18106]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 2. First order equations. Section 10 (Linear equations). Problems at page 82
Problem number : 2 (i)
Date solved : Monday, March 31, 2025 at 05:10:30 PM
CAS classification : [_linear]

\begin{align*} x \ln \left (x \right ) y^{\prime }+y&=3 x^{3} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

ode:=x*ln(x)*diff(y(x),x)+y(x) = 3*x^3; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 16

ode=(x*Log[x])*D[y[x],x]+y[x]==3*x^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.243 (sec). Leaf size: 10

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x**3 + x*log(x)*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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