12.19.10 problem section 9.3, problem 10

Internal problem ID [2157]
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 10
Date solved : Tuesday, March 04, 2025 at 01:50:55 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-5 y^{\prime \prime }+3 y^{\prime }+9 y&=2 \,{\mathrm e}^{3 x} \left (11-24 x \right ) \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 35

ode:=diff(diff(diff(y(x),x),x),x)-5*diff(diff(y(x),x),x)+3*diff(y(x),x)+9*y(x) = 2*exp(3*x)*(11-24*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-8 x^{3}+4 x c_3 +17 x^{2}+4 c_2 \right ) {\mathrm e}^{3 x}}{4}+{\mathrm e}^{-x} c_1 \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 46

ode=D[y[x],{x,3}]-5*D[y[x],{x,2}]+3*D[y[x],x]+9*y[x]==2*Exp[3*x]*(11-24*x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{3 x} \left (-2 x^3+\frac {17 x^2}{4}+\left (-\frac {17}{8}+c_3\right ) x+\frac {17}{32}+c_2\right )+c_1 e^{-x} \]

✓ Sympy. Time used: 0.335 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((48*x - 22)*exp(3*x) + 9*y(x) + 3*Derivative(y(x), x) - 5*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{3} e^{- x} + \left (C_{1} + x \left (C_{2} - 2 x^{2} + \frac {17 x}{4}\right )\right ) e^{3 x} \]