12.19.61 problem section 9.3, problem 61

Internal problem ID [2208]
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 61
Date solved : Tuesday, March 04, 2025 at 01:51:46 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-2 y&=-{\mathrm e}^{3 x} \left (17 x^{2}+67 x +9\right ) \end{align*}

✓ Maple. Time used: 0.008 (sec). Leaf size: 41

ode:=diff(diff(diff(y(x),x),x),x)+diff(diff(y(x),x),x)-2*y(x) = -exp(3*x)*(17*x^2+67*x+9); 
dsolve(ode,y(x), singsol=all);
 

\[ y = -\frac {\left (\left (x^{2}+2 x -2\right ) {\mathrm e}^{4 x}-2 c_1 \,{\mathrm e}^{2 x}-2 c_2 \cos \left (x \right )-2 c_3 \sin \left (x \right )\right ) {\mathrm e}^{-x}}{2} \]

✓ Mathematica. Time used: 0.007 (sec). Leaf size: 49

ode=D[y[x],{x,3}]+1*D[y[x],{x,2}]-0*D[y[x],x]-2*y[x]==-Exp[3*x]*(9+67*x+17*x^2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.227 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((17*x**2 + 67*x + 9)*exp(3*x) - 2*y(x) + Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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