28.2.37 problem 37

Internal problem ID [4480]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 37
Date solved : Sunday, March 30, 2025 at 03:23:38 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }+5 y&=4 \,{\mathrm e}^{x} \cos \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 24

ode:=diff(diff(y(x),x),x)-2*diff(y(x),x)+5*y(x) = 4*exp(x)*cos(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{x} \left (\left (c_1 +\frac {1}{2}\right ) \cos \left (2 x \right )+\sin \left (2 x \right ) \left (c_2 +x \right )\right ) \]

✓ Mathematica. Time used: 0.044 (sec). Leaf size: 34

ode=D[y[x],{x,2}]-2*D[y[x],x]+5*y[x]==4*Exp[x]*Cos[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

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

✓ Sympy. Time used: 0.256 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(5*y(x) - 4*exp(x)*cos(2*x) - 2*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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