Internal problem ID [14607]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.4, page 163
Problem number: 32.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+9 y=\tan \left (3 t \right )^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(diff(y(t),t$2)+9*y(t)=tan(3*t)^2,y(t), singsol=all)
\[ y \left (t \right ) = c_{2} \sin \left (3 t \right )+c_{1} \cos \left (3 t \right )+\frac {\sin \left (3 t \right ) \ln \left (\sec \left (3 t \right )+\tan \left (3 t \right )\right )}{9}-\frac {2}{9} \]
✓ Solution by Mathematica
Time used: 0.224 (sec). Leaf size: 36
DSolve[y''[t]+9*y[t]==Tan[3*t]^2,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{9} \sin (3 t) \text {arctanh}(\sin (3 t))+c_1 \cos (3 t)+c_2 \sin (3 t)-\frac {2}{9} \]