6.19.63 problem section 9.3, problem 63

Internal problem ID [2210]
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 63
Date solved : Tuesday, September 30, 2025 at 05:25:03 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }&=-2 \,{\mathrm e}^{-x} \left (6 x^{2}-18 x +7\right ) \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 37

ode:=diff(diff(diff(y(x),x),x),x)+2*diff(diff(y(x),x),x)+diff(y(x),x) = -2*exp(-x)*(6*x^2-18*x+7); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.063 (sec). Leaf size: 42

ode=D[y[x],{x,3}]+2*D[y[x],{x,2}]+1*D[y[x],x]-0*y[x]==-2*Exp[-x]*(7-18*x+6*x^2); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.208 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((12*x**2 - 36*x + 14)*exp(-x) + Derivative(y(x), x) + 2*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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