78.9.1 problem 1 (a and b)

Internal problem ID [18170]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 14. Introduction. Problems at page 112
Problem number : 1 (a and b)
Date solved : Thursday, March 13, 2025 at 11:48:03 AM
CAS classification : [[_2nd_order, _missing_y]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 15

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

\[ y = x^{3}+\frac {1}{2} c_{1} x^{2}+c_{2} \]

✓ Mathematica. Time used: 0.026 (sec). Leaf size: 20

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

\[ y(x)\to x^3+\frac {c_1 x^2}{2}+c_2 \]

✓ Sympy. Time used: 0.268 (sec). Leaf size: 12

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

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