23.5.47 problem 47

Internal problem ID [6656]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Part II. Chapter 5. THE EQUATION IS LINEAR AND OF ORDER GREATER THAN TWO, page 410
Problem number : 47
Date solved : Tuesday, September 30, 2025 at 03:50:34 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 24

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

\[ y = {\mathrm e}^{-x} \left (\frac {1}{24} x^{4}+c_1 +c_2 x +c_3 \,x^{2}\right ) \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 34

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

\begin{align*} y(x)&\to \frac {1}{24} e^{-x} \left (x^4+24 c_3 x^2+24 c_2 x+24 c_1\right ) \end{align*}

✓ Sympy. Time used: 0.175 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x*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)
 

\[ y{\left (x \right )} = \left (C_{1} + x \left (C_{2} + x \left (C_{3} + \frac {x^{2}}{24}\right )\right )\right ) e^{- x} \]