Internal problem ID [1754]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 2.4, The method of variation of parameters. Page 154
Problem number: 1.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y-\sec \left (t \right )=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(t),t$2)+y(t)=sec(t),y(t), singsol=all)
\[ y \left (t \right ) = c_{2} \sin \left (t \right )+\cos \left (t \right ) c_{1} +\sin \left (t \right ) t -\ln \left (\sec \left (t \right )\right ) \cos \left (t \right ) \]
✓ Solution by Mathematica
Time used: 0.008 (sec). Leaf size: 22
DSolve[y''[t]+y[t]==Sec[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to (t+c_2) \sin (t)+\cos (t) (\log (\cos (t))+c_1) \\ \end{align*}