Internal problem ID [14606]
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: 31.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 55
dsolve(diff(y(t),t$2)+y(t)=sec(t/2)+csc(t/2),y(t), singsol=all)
\[ y \left (t \right ) = \sin \left (t \right ) c_{2} +\cos \left (t \right ) c_{1} -2 \sin \left (t \right ) \ln \left (\sec \left (\frac {t}{2}\right )+\tan \left (\frac {t}{2}\right )\right )+2 \sin \left (t \right ) \ln \left (\csc \left (\frac {t}{2}\right )-\cot \left (\frac {t}{2}\right )\right )+4 \cos \left (\frac {t}{2}\right )+4 \sin \left (\frac {t}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.21 (sec). Leaf size: 65
DSolve[y''[t]+y[t]==Sec[t/2]+Csc[t/2],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -2 \sin (t) \text {arctanh}\left (\sin \left (\frac {t}{2}\right )\right )+4 \sin \left (\frac {t}{2}\right )+4 \cos \left (\frac {t}{2}\right )+2 \sin (t) \log \left (\sin \left (\frac {t}{4}\right )\right )+c_1 \cos (t)+c_2 \sin (t)-2 \sin (t) \log \left (\cos \left (\frac {t}{4}\right )\right ) \]