88.19.7 problem 7

Internal problem ID [24135]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 5. Special Techniques for Linear Equations. Exercises at page 139
Problem number : 7
Date solved : Thursday, October 02, 2025 at 10:00:07 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.002 (sec). Leaf size: 28

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

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

✓ Mathematica. Time used: 0.033 (sec). Leaf size: 34

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

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

✓ Sympy. Time used: 0.348 (sec). Leaf size: 36

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

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