17.8.1 problem 1.2-3 (a)

Internal problem ID [3453]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.2-3, page 12
Problem number : 1.2-3 (a)
Date solved : Monday, January 27, 2025 at 07:37:14 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }+4 \tan \left (2 t \right ) y&=\tan \left (2 t \right ) \end{align*}

With initial conditions

\begin{align*} y \left (\frac {\pi }{8}\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.032 (sec). Leaf size: 12

dsolve([diff(y(t),t)+4*tan(2*t)*y(t)=tan(2*t),y(1/8*Pi) = 2],y(t), singsol=all)
 

\[ y = 2+\frac {7 \cos \left (4 t \right )}{4} \]

✓ Solution by Mathematica

Time used: 0.088 (sec). Leaf size: 15

DSolve[{D[y[t],t]+4*Tan[2*t]*y[t]==Tan[2*t],y[Pi/8]==2},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {7}{4} \cos (4 t)+2 \]