58.1.7 problem 3(a)

Internal problem ID [14533]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 1, Differential equations and their solutions. Exercises page 13
Problem number : 3(a)
Date solved : Thursday, October 02, 2025 at 09:38:19 AM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 14

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

\[ y = \left (x^{3}+c_1 \right ) {\mathrm e}^{-3 x} \]

✓ Mathematica. Time used: 0.036 (sec). Leaf size: 17

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

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

✓ Sympy. Time used: 0.101 (sec). Leaf size: 12

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

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