10.10.9 problem 9

Internal problem ID [1341]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Chapter 3, Second order linear equations, section 3.6, Variation of Parameters. page 190
Problem number : 9
Date solved : Monday, January 27, 2025 at 04:51:39 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y&=2 \sec \left (\frac {t}{2}\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 33

dsolve(diff(y(t),t$2)+y(t) = 2*sec(t/2),y(t), singsol=all)
 

\[ y = -4 \sin \left (t \right ) \ln \left (\sec \left (\frac {t}{2}\right )+\tan \left (\frac {t}{2}\right )\right )+\sin \left (t \right ) c_2 +\cos \left (t \right ) c_1 +8 \cos \left (\frac {t}{2}\right ) \]

✓ Solution by Mathematica

Time used: 0.084 (sec). Leaf size: 35

DSolve[D[y[t],{t,2}]+y[t]== 2*Sec[t/2],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -4 \sin (t) \text {arctanh}\left (\sin \left (\frac {t}{2}\right )\right )+8 \cos \left (\frac {t}{2}\right )+c_1 \cos (t)+c_2 \sin (t) \]