63.12.1 problem 1(a)

Internal problem ID [13163]
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)
Date solved : Tuesday, January 28, 2025 at 05:11:35 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} x^{\prime \prime }+x&=\tan \left (t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 23

dsolve(diff(x(t),t$2)+x(t)=tan(t),x(t), singsol=all)
 

\[ x \left (t \right ) = c_{2} \sin \left (t \right )+\cos \left (t \right ) c_{1} -\cos \left (t \right ) \ln \left (\sec \left (t \right )+\tan \left (t \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 41

DSolve[D[x[t],{t,2}]+x[t]==Tan[t],x[t],t,IncludeSingularSolutions -> True]
 

\[ x(t)\to \sin (t) \int _1^t\sin (K[1])dK[1]+\cos (t) (-\text {arctanh}(\sin (t)))+\sin (t) \cos (t)+c_1 \cos (t)+c_2 \sin (t) \]