10.10.5 problem 5

Internal problem ID [1337]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, section 3.6, Variation of Parameters. page 190
Problem number : 5
Date solved : Monday, January 27, 2025 at 04:51:21 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 23

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

\[ y = \sin \left (t \right ) c_2 +\cos \left (t \right ) c_1 -\cos \left (t \right ) \ln \left (\sec \left (t \right )+\tan \left (t \right )\right ) \]

✓ 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]
 

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