50.3.7 problem 1(g)

Internal problem ID [7831]
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 : 1(g)
Date solved : Wednesday, March 05, 2025 at 05:07:24 AM
CAS classification : [_linear]

\begin{align*} x y^{\prime }-3 y&=x^{4} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 11

ode:=x*diff(y(x),x)-3*y(x) = x^4; 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 13

ode=x*D[y[x],x]-3*y[x]==x^4; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x^3 (x+c_1) \]

✓ Sympy. Time used: 0.234 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**4 + x*Derivative(y(x), x) - 3*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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