Internal problem ID [14703]
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: 28.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+y^{\prime }=\sec \left (t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 0, y^{\prime \prime }\left (0\right ) = 1] \end {align*}
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 84
dsolve([diff(y(t),t$3)+diff(y(t),t)=sec(t),y(0) = 0, D(y)(0) = 0, (D@@2)(y)(0) = 1],y(t), singsol=all)
\[ y \left (t \right ) = 1-\sin \left (t \right ) \ln \left (\frac {{\mathrm e}^{i t}}{{\mathrm e}^{2 i t}+1}\right )-\frac {i {\mathrm e}^{-i t}}{2}-2 i \arctan \left ({\mathrm e}^{i t}\right )+\frac {i {\mathrm e}^{i t}}{2}-t \cos \left (t \right )-\cos \left (t \right )-\ln \left (2\right ) \sin \left (t \right )+\sin \left (t \right )+\frac {i \pi }{2} \]
✓ Solution by Mathematica
Time used: 0.065 (sec). Leaf size: 52
DSolve[{y'''[t]+y'[t]==Sec[t],{y[0]==0,y'[0]==0,y''[0]==1}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -((t+1) \cos (t))-\log \left (\cos \left (\frac {t}{2}\right )-\sin \left (\frac {t}{2}\right )\right )+\log \left (\sin \left (\frac {t}{2}\right )+\cos \left (\frac {t}{2}\right )\right )+\sin (t) \log (\cos (t))+1 \]