49.11.9 problem 1(i)

Internal problem ID [7673]
Book : An introduction to Ordinary Differential Equations. Earl A. Coddington. Dover. NY 1961
Section : Chapter 2. Linear equations with constant coefficients. Page 93
Problem number : 1(i)
Date solved : Wednesday, March 05, 2025 at 04:50:16 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.006 (sec). Leaf size: 24

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

\[ y = {\mathrm e}^{-x} \left (\frac {1}{60} x^{5}+c_{1} +c_{2} x +c_3 \,x^{2}\right ) \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 34

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

\[ y(x)\to \frac {1}{60} e^{-x} \left (x^5+60 c_3 x^2+60 c_2 x+60 c_1\right ) \]

✓ Sympy. Time used: 0.364 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = \left (C_{1} + x \left (C_{2} + x \left (C_{3} + \frac {x^{3}}{60}\right )\right )\right ) e^{- x} \]