6.19.60 problem section 9.3, problem 60

Internal problem ID [2207]
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 60
Date solved : Tuesday, September 30, 2025 at 05:25:01 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime }+y&={\mathrm e}^{2 x} \left (10+3 x \right ) \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 27

ode:=diff(diff(diff(y(x),x),x),x)-diff(diff(y(x),x),x)-diff(y(x),x)+y(x) = exp(2*x)*(10+3*x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.004 (sec). Leaf size: 34

ode=D[y[x],{x,3}]-1*D[y[x],{x,2}]-1*D[y[x],x]+1*y[x]==Exp[2*x]*(10+3*x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to e^{2 x} (x+1)+c_1 e^{-x}+e^x (c_3 x+c_2) \end{align*}

✓ Sympy. Time used: 0.163 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-3*x - 10)*exp(2*x) + y(x) - Derivative(y(x), x) - Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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