81.11.2 problem 15-1 (b)

Internal problem ID [21626]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 15. Method of undetermined coefficients. Page 337.
Problem number : 15-1 (b)
Date solved : Thursday, October 02, 2025 at 07:59:07 PM
CAS classification : [[_linear, `class A`]]

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

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

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

\[ y = -3 x^{2}-7 x -7+{\mathrm e}^{x} c_1 \]

✓ Mathematica. Time used: 0.074 (sec). Leaf size: 21

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

\begin{align*} y(x)&\to -3 x^2-7 x+c_1 e^x-7 \end{align*}

✓ Sympy. Time used: 0.072 (sec). Leaf size: 17

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

\[ y{\left (x \right )} = C_{1} e^{x} - 3 x^{2} - 7 x - 7 \]