Internal problem ID [14612]
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: 37.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+4 y=\tan \left (t \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(diff(y(t),t$2)+4*y(t)=tan(t),y(t), singsol=all)
\[ y \left (t \right ) = \sin \left (t \right ) \cos \left (t \right ) \ln \left (\cos \left (t \right )\right )+\left (2 c_{1} -t \right ) \cos \left (t \right )^{2}+\frac {\sin \left (t \right ) \left (4 c_{2} +1\right ) \cos \left (t \right )}{2}-c_{1} +\frac {t}{2} \]
✓ Solution by Mathematica
Time used: 0.05 (sec). Leaf size: 38
DSolve[y''[t]+4*y[t]==Tan[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{4} (\sin (2 t) (2 \log (\cos (t))-1+4 c_2)-2 (t-2 c_1) \cos (2 t)) \]