Internal problem ID [1973]
Book: Ordinary Differential Equations, Robert H. Martin, 1983
Section: Problem 1.2-3, page 12
Problem number: 1.2-3 (a).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }+4 \tan \left (2 t \right ) y-\tan \left (2 t \right )=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {\pi }{8}\right ) = 2\right ] \end {align*}
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 14
dsolve([diff(y(t),t)+4*tan(2*t)*y(t)=tan(2*t),y(1/8*Pi) = 2],y(t), singsol=all)
\[ y \relax (t ) = \frac {7 \left (\cos ^{2}\left (2 t \right )\right )}{2}+\frac {1}{4} \]
✓ Solution by Mathematica
Time used: 0.103 (sec). Leaf size: 15
DSolve[{y'[t]+4*Tan[2*t]*y[t]==Tan[2*t],y[Pi/8]==2},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to \frac {7}{4} \cos (4 t)+2 \\ \end{align*}