Internal problem ID [14581]
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: 6.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+\frac {y}{4}=\sec \left (\frac {t}{2}\right )+\csc \left (\frac {t}{2}\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 48
dsolve(diff(y(t),t$2)+1/4*y(t)=sec(t/2)+csc(t/2),y(t), singsol=all)
\[ y \left (t \right ) = 4 \cos \left (\frac {t}{2}\right ) \ln \left (\cos \left (\frac {t}{2}\right )\right )+4 \sin \left (\frac {t}{2}\right ) \ln \left (\sin \left (\frac {t}{2}\right )\right )+\left (c_{1} -2 t \right ) \cos \left (\frac {t}{2}\right )+2 \left (t +\frac {c_{2}}{2}\right ) \sin \left (\frac {t}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.066 (sec). Leaf size: 50
DSolve[y''[t]+1/4*y[t]==Sec[t/2]+Csc[t/2],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \cos \left (\frac {t}{2}\right ) \left (-2 t+4 \log \left (\cos \left (\frac {t}{2}\right )\right )+c_1\right )+\sin \left (\frac {t}{2}\right ) \left (2 t+4 \log \left (\sin \left (\frac {t}{2}\right )\right )+c_2\right ) \]