14.7.5 problem Problem 29

Internal problem ID [3720]
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 8.3, The Method of Undetermined Coefficients. page 525
Problem number : Problem 29
Date solved : Tuesday, September 30, 2025 at 06:56:20 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&=3 \sin \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 36

ode:=diff(diff(y(x),x),x)+2*diff(y(x),x)+5*y(x) = 3*sin(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\sin \left (2 x \right ) \left (17 c_2 \,{\mathrm e}^{-x}+3\right )}{17}+{\mathrm e}^{-x} \cos \left (2 x \right ) c_1 -\frac {12 \cos \left (2 x \right )}{17} \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 45

ode=D[y[x],{x,2}]+2*D[y[x],x]+5*y[x]==3*Sin[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{17} e^{-x} \left (\left (-12 e^x+17 c_2\right ) \cos (2 x)+\left (3 e^x+17 c_1\right ) \sin (2 x)\right ) \end{align*}

✓ Sympy. Time used: 0.146 (sec). Leaf size: 36

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*y(x) - 3*sin(2*x) + 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \left (C_{1} \sin {\left (2 x \right )} + C_{2} \cos {\left (2 x \right )}\right ) e^{- x} + \frac {3 \sin {\left (2 x \right )}}{17} - \frac {12 \cos {\left (2 x \right )}}{17} \]