Internal problem ID [687]
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: 5.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y=\tan \left (t \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 23
dsolve(diff(y(t),t$2)+y(t) = tan(t),y(t), singsol=all)
\[ y \left (t \right ) = c_{2} \sin \left (t \right )+\cos \left (t \right ) c_{1} -\cos \left (t \right ) \ln \left (\sec \left (t \right )+\tan \left (t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.04 (sec). Leaf size: 23
DSolve[y''[t]+y[t] == Tan[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to \cos (t) (-\text {arctanh}(\sin (t)))+c_1 \cos (t)+c_2 \sin (t) \]