64.5.3 problem 3

Internal problem ID [13245]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, section 2.3 (Linear equations). Exercises page 56
Problem number : 3
Date solved : Monday, March 31, 2025 at 07:43:19 AM
CAS classification : [[_linear, `class A`]]

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

✓ Maple. Time used: 0.001 (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: 0.071 (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]
 

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

✓ Sympy. Time used: 0.185 (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)
 

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