78.5.18 problem 4 (g)

Internal problem ID [18090]
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 9 (Integrating Factors). Problems at page 80
Problem number : 4 (g)
Date solved : Monday, March 31, 2025 at 05:07:48 PM
CAS classification : [_linear]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 14

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

\[ y = c_1 x +2 x^{2}+3 \]

✓ Mathematica. Time used: 0.031 (sec). Leaf size: 16

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

\[ y(x)\to 2 x^2+c_1 x+3 \]

✓ Sympy. Time used: 0.217 (sec). Leaf size: 12

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

\[ y{\left (x \right )} = C_{1} x + 2 x^{2} + 3 \]