33.3.1 problem Problem 12.1

Internal problem ID [7814]
Book : Schaums Outline Differential Equations, 4th edition. Bronson and Costa. McGraw Hill 2014
Section : Chapter 12. VARIATION OF PARAMETERS. page 104
Problem number : Problem 12.1
Date solved : Tuesday, September 30, 2025 at 05:05:52 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime }&=\sec \left (x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 55

ode:=diff(diff(diff(y(x),x),x),x)+diff(y(x),x) = sec(x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {{\mathrm e}^{-i x} \left (-i \ln \left (\sec \left (x \right )\right )+i c_1 -c_2 -x \right )}{2}+\frac {{\mathrm e}^{i x} \left (i \ln \left (\sec \left (x \right )\right )-i c_1 -c_2 -x \right )}{2}-2 i \arctan \left ({\mathrm e}^{i x}\right )+c_3 \]

✓ Mathematica. Time used: 60.022 (sec). Leaf size: 36

ode=D[y[x],{x,3}]+D[y[x],x]==Sec[x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \int _1^x(\cos (K[1]) (c_1+\log (\cos (K[1])))+(c_2+K[1]) \sin (K[1]))dK[1]+c_3 \end{align*}

✓ Sympy. Time used: 0.205 (sec). Leaf size: 37

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) + Derivative(y(x), (x, 3)) - 1/cos(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} + \left (C_{2} - x\right ) \cos {\left (x \right )} + \left (C_{3} + \log {\left (\cos {\left (x \right )} \right )}\right ) \sin {\left (x \right )} - \frac {\log {\left (\sin {\left (x \right )} - 1 \right )}}{2} + \frac {\log {\left (\sin {\left (x \right )} + 1 \right )}}{2} \]