20.8.10 problem Problem 10

Internal problem ID [3743]
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 10
Date solved : Sunday, March 30, 2025 at 02:07:05 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+10 y&=24 \,{\mathrm e}^{x} \cos \left (3 x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 31

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)+10*y(x) = 24*exp(x)*cos(3*x); 
dsolve(ode,y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.047 (sec). Leaf size: 36

ode=D[y[x],{x,2}]-2*D[y[x],x]+10*y[x]==24*Exp[x]*Cos[3*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{3} e^x ((2+3 c_2) \cos (3 x)+3 (4 x+c_1) \sin (3 x)) \]

✓ Sympy. Time used: 0.252 (sec). Leaf size: 22

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(10*y(x) - 24*exp(x)*cos(3*x) - 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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