6.19.9 problem section 9.3, problem 9

Internal problem ID [2156]
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 9
Date solved : Tuesday, September 30, 2025 at 05:24:27 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} 2 y^{\prime \prime \prime }-7 y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{2 x} \left (17+30 x \right ) \end{align*}

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

ode:=2*diff(diff(diff(y(x),x),x),x)-7*diff(diff(y(x),x),x)+4*diff(y(x),x)+4*y(x) = exp(2*x)*(17+30*x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 46

ode=2*D[y[x],{x,3}]-7*D[y[x],{x,2}]+4*D[y[x],x]+4*y[x]==Exp[2*x]*(17+30*x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.235 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-30*x - 17)*exp(2*x) + 4*y(x) + 4*Derivative(y(x), x) - 7*Derivative(y(x), (x, 2)) + 2*Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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