50.17.12 problem 1(f) solving directly

Internal problem ID [8083]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 4. Power Series Solutions and Special Functions. Section 4.2. Series Solutions of First-Order Differential Equations Page 162
Problem number : 1(f) solving directly
Date solved : Sunday, March 30, 2025 at 12:44:56 PM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (sec). Leaf size: 18

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

\[ y = -x^{2}-2 x -2+{\mathrm e}^{x} c_1 \]

✓ Mathematica. Time used: 0.03 (sec). Leaf size: 21

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

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

✓ Sympy. Time used: 0.119 (sec). Leaf size: 15

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

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