14.8.2 problem Problem 2

Internal problem ID [3735]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.4, Complex-Valued Trial Solutions. page 529
Problem number : Problem 2
Date solved : Tuesday, September 30, 2025 at 06:56:31 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+y&=50 \sin \left (3 x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 27

ode:=diff(diff(y(x),x),x)+2*diff(y(x),x)+y(x) = 50*sin(3*x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 34

ode=D[y[x],{x,2}]+2*D[y[x],x]+y[x]==50*Sin[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.146 (sec). Leaf size: 24

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - 50*sin(3*x) + 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} + C_{2} x\right ) e^{- x} - 4 \sin {\left (3 x \right )} - 3 \cos {\left (3 x \right )} \]