15.12.1 problem 1

Internal problem ID [3145]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 20, page 90
Problem number : 1
Date solved : Monday, January 27, 2025 at 07:23:34 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 22

dsolve(diff(y(x),x$2)+y(x)=sec(x),y(x), singsol=all)
 

\[ y = -\cos \left (x \right ) \ln \left (\sec \left (x \right )\right )+\cos \left (x \right ) c_{1} +\sin \left (x \right ) \left (c_2 +x \right ) \]

✓ Solution by Mathematica

Time used: 0.020 (sec). Leaf size: 22

DSolve[D[y[x],{x,2}]+y[x]==Sec[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to (x+c_2) \sin (x)+\cos (x) (\log (\cos (x))+c_1) \]