74.18.40 problem 46

Internal problem ID [16597]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number : 46
Date solved : Tuesday, January 28, 2025 at 09:12:13 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&=\tan \left (2 t \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

dsolve(diff(y(t),t$2)+4*y(t)=tan(2*t),y(t), singsol=all)
 

\[ y = \sin \left (2 t \right ) c_{2} +\cos \left (2 t \right ) c_{1} -\frac {\cos \left (2 t \right ) \ln \left (\sec \left (2 t \right )+\tan \left (2 t \right )\right )}{4} \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 40

DSolve[D[y[t],{t,2}]+4*y[t]==Tan[2*t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {1}{4} \cos (2 t) \text {arctanh}(\sin (2 t))+c_1 \cos (2 t)+\frac {1}{4} (-1+4 c_2) \sin (2 t) \]