Internal problem ID [6329]
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(g).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\sec \left (x \right ) \csc \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(diff(y(x),x$2)+y(x)=sec(x)*csc(x),y(x), singsol=all)
\[ y \left (x \right ) = \sin \left (x \right ) c_{2} +\cos \left (x \right ) c_{1} +\sin \left (x \right ) \ln \left (\csc \left (x \right )-\cot \left (x \right )\right )-\cos \left (x \right ) \ln \left (\sec \left (x \right )+\tan \left (x \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 30
DSolve[y''[x]+y[x]==Sec[x]*Csc[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\sin (x) \text {arctanh}(\cos (x))+c_1 \cos (x)+c_2 \sin (x)+\cos (x) \left (-\coth ^{-1}(\sin (x))\right ) \]