87.18.8 problem 8

Internal problem ID [23649]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 2. Linear differential equations. Exercise at page 135
Problem number : 8
Date solved : Thursday, October 02, 2025 at 09:43:49 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

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

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

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

✓ Mathematica. Time used: 0.027 (sec). Leaf size: 28

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

\begin{align*} y(x)&\to e^{-2 x} ((x+c_1) \sin (x)+\cos (x) (\log (\cos (x))+c_2)) \end{align*}

✓ Sympy. Time used: 0.368 (sec). Leaf size: 24

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

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