Internal problem ID [14618]
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: 43.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\tan \left (t \right )^{2}} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 21
dsolve([diff(y(t),t$2)+y(t)=tan(t)^2,y(0) = 0, D(y)(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = \sin \left (t \right )+2 \cos \left (t \right )-2+\sin \left (t \right ) \ln \left (\sec \left (t \right )+\tan \left (t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.117 (sec). Leaf size: 19
DSolve[{y''[t]+y[t]==Tan[t]^2,{y[0]==0,y'[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \sin (t) \text {arctanh}(\sin (t))+\sin (t)+2 \cos (t)-2 \]