44.17.12 problem 1(f) solving directly

Internal problem ID [9369]
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 : Tuesday, September 30, 2025 at 06:17:51 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: 0.022 (sec). Leaf size: 30

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

\begin{align*} y(x)&\to e^x \left (\int _1^xe^{-K[1]} K[1]^2dK[1]+c_1\right ) \end{align*}

✓ Sympy. Time used: 0.067 (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)
 

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