Internal problem ID [6323]
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(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\sec \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(diff(y(x),x$2)+y(x)=sec(x),y(x), singsol=all)
\[ y \left (x \right ) = -\ln \left (\sec \left (x \right )\right ) \cos \left (x \right )+\cos \left (x \right ) c_{1} +\left (x +c_{2} \right ) \sin \left (x \right ) \]
✓ Solution by Mathematica
Time used: 0.035 (sec). Leaf size: 22
DSolve[y''[x]+y[x]==Sec[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to (x+c_2) \sin (x)+\cos (x) (\log (\cos (x))+c_1) \]