Internal problem ID [14686]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.6, page 187
Problem number: 11.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+4 y^{\prime }=\tan \left (2 t \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 90
dsolve(diff(y(t),t$3)+4*diff(y(t),t)=tan(2*t),y(t), singsol=all)
\[ y \left (t \right ) = \frac {i \left ({\mathrm e}^{2 i t}-{\mathrm e}^{-2 i t}\right ) \ln \left (\frac {i {\mathrm e}^{2 i t}-1}{-{\mathrm e}^{2 i t}+i}\right )}{16}+\frac {\sin \left (2 t \right ) c_{1}}{2}-\frac {c_{2} \cos \left (2 t \right )}{2}+\frac {\ln \left ({\mathrm e}^{i t}\right )}{4}-\frac {\ln \left ({\mathrm e}^{2 i t}-i\right )}{8}-\frac {\ln \left ({\mathrm e}^{2 i t}+i\right )}{8}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.167 (sec). Leaf size: 53
DSolve[y'''[t]+4*y'[t]==Tan[2*t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \frac {1}{16} \left (-2 \sin (2 t) \text {arctanh}(\sin (2 t))-\log \left (\cos ^2(2 t)\right )+(2-8 c_2) \cos (2 t)+8 c_1 \sin (2 t)+16 c_3\right ) \]