89.19.25 problem 25

Internal problem ID [24753]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 10. Nonhomogeneous Equations: Operational methods. Exercises at page 151
Problem number : 25
Date solved : Thursday, October 02, 2025 at 10:47:41 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 16

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

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

✓ Mathematica. Time used: 0.053 (sec). Leaf size: 24

ode=D[y[x],{x,2}]-2*D[y[x],{x,1}]+y[x]== Exp[x]*Sec[x]^2*Tan[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{2} e^x (\tan (x)+2 (c_2 x+c_1)) \end{align*}

✓ Sympy. Time used: 0.443 (sec). Leaf size: 15

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

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