Internal problem ID [11497]
Book: A First Course in Differential Equations by J. David Logan. Third Edition. Springer-Verlag,
NY. 2015.
Section: Chapter 2, Second order linear equations. Section 2.4.2 Variation of parameters.
Exercises page 124
Problem number: 1(a).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {x^{\prime \prime }+x=\tan \left (t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(x(t),t$2)+x(t)=tan(t),x(t), singsol=all)
\[ x \left (t \right ) = \sin \left (t \right ) c_{2} +c_{1} \cos \left (t \right )-\cos \left (t \right ) \ln \left (\sec \left (t \right )+\tan \left (t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.053 (sec). Leaf size: 23
DSolve[x''[t]+x[t]==Tan[t],x[t],t,IncludeSingularSolutions -> True]
\[ x(t)\to \cos (t) (-\text {arctanh}(\sin (t)))+c_1 \cos (t)+c_2 \sin (t) \]