Internal problem ID [5575]
Book: Differential Equations: Theory, Technique, and Practice by George Simmons, Steven Krantz.
McGraw-Hill NY. 2007. 1st Edition.
Section: Chapter 2. Second-Order Linear Equations. Section 2.3. THE METHOD OF VARIATION OF
PARAMETERS. Page 71
Problem number: 2(f).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+y-\sec \relax (x ) \tan \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)+y(x)=sec(x)*tan(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} \sin \relax (x )+c_{1} \cos \relax (x )+\left (\ln \left (\frac {1}{\cos \relax (x )}\right )-1\right ) \sin \relax (x )+x \cos \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.026 (sec). Leaf size: 25
DSolve[y''[x]+y[x]==Sec[x]*Tan[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to (x+c_1) \cos (x)+\sin (x) (-\log (\cos (x))-1+c_2) \\ \end{align*}