50.3.13 problem 2(c)

Internal problem ID [7837]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 1. What is a differential equation. Section 1.4 First Order Linear Equations. Page 15
Problem number : 2(c)
Date solved : Wednesday, March 05, 2025 at 05:07:29 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (1\right )&=0 \end{align*}

✗ Maple

ode:=x*ln(x)*diff(y(x),x)+y(x) = 3*x^3; 
ic:=y(1) = 0; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=(x*Log[x])*D[y[x],x]+y[x]==3*x^3; 
ic={y[1]==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✓ Sympy. Time used: 0.263 (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 = {y(1): 0} 
dsolve(ode,func=y(x),ics=ics)
 

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