10.10.6 problem 6

Internal problem ID [1338]
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 : 6
Date solved : Monday, January 27, 2025 at 04:51:25 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=9 \sec \left (3 t \right )^{2} \end{align*}

✓ Solution by Maple

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

dsolve(diff(y(t),t$2)+9*y(t) = 9*sec(3*t)^2,y(t), singsol=all)
 

\[ y = \sin \left (3 t \right ) c_2 +\cos \left (3 t \right ) c_1 +\ln \left (\sec \left (3 t \right )+\tan \left (3 t \right )\right ) \sin \left (3 t \right )-1 \]

✓ Solution by Mathematica

Time used: 0.082 (sec). Leaf size: 31

DSolve[D[y[t],{t,2}]+9*y[t] == 9*Sec[3*t]^2,y[t],t,IncludeSingularSolutions -> True]
 

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