Internal problem ID [4135]
Book: Ordinary Differential Equations, By Tenenbaum and Pollard. Dover, NY 1963
Section: Chapter 4. Higher order linear differential equations. Lesson 22. Variation of Parameters
Problem number: Exercise 22.13, page 240.
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 ) \csc \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 42
dsolve(diff(y(x),x$2)+y(x)=sec(x)*csc(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} \sin \relax (x )+c_{1} \cos \relax (x )+\sin \relax (x ) \ln \left (\frac {1-\cos \relax (x )}{\sin \relax (x )}\right )-\ln \left (\frac {1+\sin \relax (x )}{\cos \relax (x )}\right ) \cos \relax (x ) \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 66
DSolve[y''[x]+y[x]==Sec[x]*Csc[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \cos (x) \left (\log \left (\cos \left (\frac {x}{2}\right )-\sin \left (\frac {x}{2}\right )\right )-\log \left (\sin \left (\frac {x}{2}\right )+\cos \left (\frac {x}{2}\right )\right )+c_1\right )+\sin (x) \left (\log \left (\sin \left (\frac {x}{2}\right )\right )-\log \left (\cos \left (\frac {x}{2}\right )\right )+c_2\right ) \\ \end{align*}