Internal problem ID [518]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.4. Page 76
Problem number: 3.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {\tan \relax (t ) y+y^{\prime }-\sin \relax (t )=0} \end {gather*} With initial conditions \begin {align*} [y \left (\pi \right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve([tan(t)*y(t)+diff(y(t),t) = sin(t),y(Pi) = 0],y(t), singsol=all)
\[ y \relax (t ) = \left (-\ln \left (\cos \relax (t )\right )+i \pi \right ) \cos \relax (t ) \]
✓ Solution by Mathematica
Time used: 0.078 (sec). Leaf size: 20
DSolve[{Tan[t]*y[t]+y'[t] == Sin[t],y[Pi]==0},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to i \cos (t) (\pi +i \log (\cos (t))) \\ \end{align*}