23.5.28 problem 28

Internal problem ID [6637]
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 : 28
Date solved : Tuesday, September 30, 2025 at 03:50:25 PM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 27

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

\[ y = \frac {{\mathrm e}^{2 x} c_2}{2}+c_3 +\frac {{\mathrm e}^{-x} \left (-6 c_1 +2 x +2\right )}{6} \]

✓ Mathematica. Time used: 0.058 (sec). Leaf size: 37

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

\begin{align*} y(x)&\to \frac {1}{9} e^{-x} (3 x+4-9 c_1)+\frac {1}{2} c_2 e^{2 x}+c_3 \end{align*}

✓ Sympy. Time used: 0.141 (sec). Leaf size: 19

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

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