85.67.14 problem 14

Internal problem ID [22905]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 216
Problem number : 14
Date solved : Thursday, October 02, 2025 at 09:16:27 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \\ y^{\prime }\left (0\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.011 (sec). Leaf size: 20

ode:=diff(diff(y(x),x),x)+y(x) = sec(x); 
ic:=[y(0) = 1, D(y)(0) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\ln \left (\sec \left (x \right )\right ) \cos \left (x \right )+\cos \left (x \right )+\left (x +2\right ) \sin \left (x \right ) \]

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 20

ode=D[y[x],{x,2}]+y[x]==Sec[x]; 
ic={y[0]==1,Derivative[1][y][0] ==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to (x+2) \sin (x)+\cos (x) (\log (\cos (x))+1) \end{align*}

✓ Sympy. Time used: 0.145 (sec). Leaf size: 19

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - sec(x) + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 1, Subs(Derivative(y(x), x), x, 0): 2} 
dsolve(ode,func=y(x),ics=ics)
 

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