Internal problem ID [691]
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.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=2 \sec \left (\frac {t}{2}\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(t),t$2)+y(t) = 2*sec(t/2),y(t), singsol=all)
\[ y \left (t \right ) = -4 \sin \left (t \right ) \ln \left (\sec \left (\frac {t}{2}\right )+\tan \left (\frac {t}{2}\right )\right )+c_{2} \sin \left (t \right )+\cos \left (t \right ) c_{1} +8 \cos \left (\frac {t}{2}\right ) \]
✓ Solution by Mathematica
Time used: 0.114 (sec). Leaf size: 35
DSolve[y''[t]+y[t]== 2*Sec[t/2],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -4 \sin (t) \text {arctanh}\left (\sin \left (\frac {t}{2}\right )\right )+8 \cos \left (\frac {t}{2}\right )+c_1 \cos (t)+c_2 \sin (t) \]