20.8.6 problem Problem 6

Internal problem ID [3739]
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 6
Date solved : Sunday, March 30, 2025 at 02:06:58 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 28

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

\[ y = \sin \left (x \right ) c_2 +\cos \left (x \right ) c_1 -\frac {3 \,{\mathrm e}^{x} \left (-2 \sin \left (2 x \right )+\cos \left (2 x \right )\right )}{10} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 34

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

\[ y(x)\to -\frac {3}{10} e^x (\cos (2 x)-2 \sin (2 x))+c_1 \cos (x)+c_2 \sin (x) \]

✓ Sympy. Time used: 0.103 (sec). Leaf size: 36

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

\[ y{\left (x \right )} = C_{1} \sin {\left (x \right )} + C_{2} \cos {\left (x \right )} + \frac {3 e^{x} \sin {\left (2 x \right )}}{5} - \frac {3 e^{x} \cos {\left (2 x \right )}}{10} \]