81.11.25 problem 15-24

Internal problem ID [21649]
Book : The Differential Equations Problem Solver. VOL. I. M. Fogiel director. REA, NY. 1978. ISBN 78-63609
Section : Chapter 15. Method of undetermined coefficients. Page 337.
Problem number : 15-24
Date solved : Thursday, October 02, 2025 at 07:59:27 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 22

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

\[ y = {\mathrm e}^{x} \left (\frac {1}{2} x^{3}+c_1 +c_2 x +c_3 \,x^{2}\right ) \]

✓ Mathematica. Time used: 0.005 (sec). Leaf size: 32

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

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

✓ Sympy. Time used: 0.138 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-y(x) - 3*exp(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)
 

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