6.19.11 problem section 9.3, problem 11

Internal problem ID [2158]
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 11
Date solved : Tuesday, September 30, 2025 at 05:24:28 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-7 y^{\prime \prime }+8 y^{\prime }+16 y&=2 \,{\mathrm e}^{4 x} \left (13+15 x \right ) \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 29

ode:=diff(diff(diff(y(x),x),x),x)-7*diff(diff(y(x),x),x)+8*diff(y(x),x)+16*y(x) = 2*exp(4*x)*(13+15*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{-x} \left (\left (x^{3}+c_3 x +2 x^{2}+c_2 \right ) {\mathrm e}^{5 x}+c_1 \right ) \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 42

ode=D[y[x],{x,3}]-7*D[y[x],{x,2}]+8*D[y[x],x]+16*y[x]==2*Exp[4*x]*(13+15*x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{4 x} \left (x^3+2 x^2+\left (-\frac {4}{5}+c_3\right ) x+\frac {4}{25}+c_2\right )+c_1 e^{-x} \end{align*}

✓ Sympy. Time used: 0.215 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-30*x - 26)*exp(4*x) + 16*y(x) + 8*Derivative(y(x), x) - 7*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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