76.17.5 problem 14

Internal problem ID [17691]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 4. Second order linear equations. Section 4.7 (Variation of parameters). Problems at page 280
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 10:59:39 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 23

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

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

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 23

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

\[ y(t)\to \cos (t) (-\text {arctanh}(\sin (t)))+c_1 \cos (t)+c_2 \sin (t) \]