Internal problem ID [14700]
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: 25.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime \prime }+y^{\prime \prime }=\tan \left (t \right )^{2}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 76
dsolve(diff(y(t),t$4)+diff(y(t),t$2)=tan(t)^2,y(t), singsol=all)
\[ y \left (t \right ) = \frac {\left (\int \left (\left (-{\mathrm e}^{-i t}-{\mathrm e}^{i t}\right ) \ln \left (\frac {i {\mathrm e}^{i t}-1}{-{\mathrm e}^{i t}+i}\right )-2 i \ln \left ({\mathrm e}^{i t}\right )+2 c_{1} \sin \left (t \right )-2 c_{2} \cos \left (t \right )-4 t \right )d t \right )}{2}+c_{3} t +c_{4} \]
✓ Solution by Mathematica
Time used: 0.169 (sec). Leaf size: 47
DSolve[y''''[t]+y''[t]==Tan[t]^2,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\sin (t) \text {arctanh}(\sin (t))-\frac {t^2}{2}+c_4 t-\frac {1}{2} \log \left (\cos ^2(t)\right )-c_1 \cos (t)-c_2 \sin (t)+c_3 \]