44.13.18 problem 17

Internal problem ID [9319]
Book : Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz. McGraw-Hill NY. 2007. 1st Edition.
Section : Chapter 2. Section 2.7. HIGHER ORDER LINEAR EQUATIONS, COUPLED HARMONIC OSCILLATORS Page 98
Problem number : 17
Date solved : Tuesday, September 30, 2025 at 06:16:23 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y^{\prime }&=10+42 \,{\mathrm e}^{3 x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 26

ode:=diff(diff(diff(y(x),x),x),x)-3*diff(diff(y(x),x),x)+2*diff(y(x),x) = 10+42*exp(3*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} c_2 +\frac {{\mathrm e}^{2 x} c_1}{2}+7 \,{\mathrm e}^{3 x}+5 x +c_3 \]

✓ Mathematica. Time used: 0.17 (sec). Leaf size: 35

ode=D[y[x],{x,3}]-3*D[y[x],{x,2}]+2*D[y[x],x]==10+42*Exp[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 5 x+7 e^{3 x}+c_1 e^x+\frac {1}{2} c_2 e^{2 x}+c_3 \end{align*}

✓ Sympy. Time used: 0.112 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-42*exp(3*x) + 2*Derivative(y(x), x) - 3*Derivative(y(x), (x, 2)) + Derivative(y(x), (x, 3)) - 10,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + C_{2} e^{x} + C_{3} e^{2 x} + 5 x + 7 e^{3 x} \]