12.19.14 problem section 9.3, problem 14

Internal problem ID [2161]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.3. Undetermined Coefficients for Higher Order Equations. Page 495
Problem number : section 9.3, problem 14
Date solved : Tuesday, March 04, 2025 at 01:50:58 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+3 y^{\prime \prime \prime }+y^{\prime \prime }-3 y^{\prime }-2 y&=-3 \,{\mathrm e}^{2 x} \left (11+12 x \right ) \end{align*}

✓ Maple. Time used: 0.009 (sec). Leaf size: 35

ode:=diff(diff(diff(diff(y(x),x),x),x),x)+3*diff(diff(diff(y(x),x),x),x)+diff(diff(y(x),x),x)-3*diff(y(x),x)-2*y(x) = -3*exp(2*x)*(11+12*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-2 x} \left (\left (1-x \right ) {\mathrm e}^{4 x}+c_1 \,{\mathrm e}^{3 x}+\left (c_4 x +c_3 \right ) {\mathrm e}^{x}+c_2 \right ) \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 43

ode=D[y[x],{x,4}]+3*D[y[x],{x,3}]+D[y[x],{x,2}]-3*D[y[x],x]-2*y[x]==-3*Exp[2*x]*(11+12*x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{-2 x} \left (-e^{4 x} (x-1)+e^x (c_3 x+c_2)+c_4 e^{3 x}+c_1\right ) \]

✓ Sympy. Time used: 0.318 (sec). Leaf size: 31

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((36*x + 33)*exp(2*x) - 2*y(x) - 3*Derivative(y(x), x) + Derivative(y(x), (x, 2)) + 3*Derivative(y(x), (x, 3)) + Derivative(y(x), (x, 4)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{3} e^{- 2 x} + C_{4} e^{x} + \left (1 - x\right ) e^{2 x} + \left (C_{1} + C_{2} x\right ) e^{- x} \]