Internal problem ID [1667]
Book: Differential equations and their applications, 3rd ed., M. Braun
Section: Section 1.2. Page 9
Problem number: 23.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }+\tan \relax (t ) y-\sin \relax (t ) \cos \relax (t )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 13
dsolve(diff(y(t),t)+tan(t)*y(t)=cos(t)*sin(t),y(t), singsol=all)
\[ y \relax (t ) = \left (-\cos \relax (t )+c_{1}\right ) \cos \relax (t ) \]
✓ Solution by Mathematica
Time used: 0.051 (sec). Leaf size: 15
DSolve[y'[t]+Tan[t]*y[t]==Cos[t]*Sin[t],y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \cos (t) (-\cos (t)+c_1) \\ \end{align*}