6.19.7 problem section 9.3, problem 7

Internal problem ID [2154]
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 7
Date solved : Tuesday, September 30, 2025 at 05:24:27 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} 4 y^{\prime \prime \prime }+8 y^{\prime \prime }-y^{\prime }-2 y&=-{\mathrm e}^{-2 x} \left (1-15 x \right ) \end{align*}

✓ Maple. Time used: 0.068 (sec). Leaf size: 34

ode:=4*diff(diff(diff(y(x),x),x),x)+8*diff(diff(y(x),x),x)-diff(y(x),x)-2*y(x) = -exp(-2*x)*(1-15*x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.052 (sec). Leaf size: 53

ode=4*D[y[x],{x,3}]+8*D[y[x],{x,2}]-D[y[x],x]-2*y[x]==-Exp[-2*x]*(1-15*x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{10} e^{-2 x} \left (5 x^2+10 x+2 \left (5 c_1 e^{3 x/2}+5 c_2 e^{5 x/2}+4+5 c_3\right )\right ) \end{align*}

✓ Sympy. Time used: 0.224 (sec). Leaf size: 29

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((1 - 15*x)*exp(-2*x) - 2*y(x) - Derivative(y(x), x) + 8*Derivative(y(x), (x, 2)) + 4*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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