Internal problem ID [688]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }+9 y-9 \left (\sec ^{2}\left (3 t \right )\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 37
dsolve(diff(y(t),t$2)+9*y(t) = 9*sec(3*t)^2,y(t), singsol=all)
\[ y \relax (t ) = c_{2} \sin \left (3 t \right )+c_{1} \cos \left (3 t \right )+\ln \left (\frac {1+\sin \left (3 t \right )}{\cos \left (3 t \right )}\right ) \sin \left (3 t \right )-1 \]
✓ Solution by Mathematica
Time used: 0.062 (sec). Leaf size: 54
DSolve[y''[t]+9*y[t] == 9*Sec[3*t]^2,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to c_1 \cos (3 t)+\sin (3 t) \left (-\log \left (\cos \left (\frac {3 t}{2}\right )-\sin \left (\frac {3 t}{2}\right )\right )+\log \left (\sin \left (\frac {3 t}{2}\right )+\cos \left (\frac {3 t}{2}\right )\right )+c_2\right )-1 \\ \end{align*}