76.17.6 problem 15

Internal problem ID [17692]
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 : 15
Date solved : Tuesday, January 28, 2025 at 10:59:42 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&=3 \sec \left (2 t \right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 34

dsolve(diff(y(t),t$2)+4*y(t)=3*sec(2*t)^2,y(t), singsol=all)
 

\[ y = \sin \left (2 t \right ) c_{2} +\cos \left (2 t \right ) c_{1} +\frac {3 \ln \left (\sec \left (2 t \right )+\tan \left (2 t \right )\right ) \sin \left (2 t \right )}{4}-\frac {3}{4} \]

✓ Solution by Mathematica

Time used: 0.061 (sec). Leaf size: 36

DSolve[D[y[t],{t,2}]+4*y[t]==3*Sec[2*t]^2,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to c_1 \cos (2 t)+\frac {3}{4} \sin (2 t) \coth ^{-1}(\sin (2 t))+c_2 \sin (2 t)-\frac {3}{4} \]