50.3.5 problem 1(e)

Internal problem ID [7829]
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(e)
Date solved : Wednesday, March 05, 2025 at 05:07:22 AM
CAS classification : [_linear]

\begin{align*} 2 y-x^{3}&=x y^{\prime } \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 13

ode:=2*y(x)-x^3 = x*diff(y(x),x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \left (-x +c_{1} \right ) x^{2} \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 15

ode=2*y[x]-x^3==x*D[y[x],x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x^2 (-x+c_1) \]

✓ Sympy. Time used: 0.229 (sec). Leaf size: 8

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**3 - x*Derivative(y(x), x) + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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