78.3.7 problem 1 (g)

Internal problem ID [18039]
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 7 (Homogeneous Equations). Problems at page 67
Problem number : 1 (g)
Date solved : Monday, March 31, 2025 at 04:59:11 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 13

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

\[ y = c_1 \,x^{3}-x \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 15

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

\[ y(x)\to x \left (-1+c_1 x^2\right ) \]

✓ Sympy. Time used: 0.205 (sec). Leaf size: 10

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

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