Internal problem ID [1976]
Book: Ordinary Differential Equations, Robert H. Martin, 1983
Section: Problem 1.2-3, page 12
Problem number: 1.2-3 (d).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
Solve \begin {gather*} \boxed {y^{\prime }+\cot \relax (t ) y-6 \left (\cos ^{2}\relax (t )\right )=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {\pi }{4}\right ) = 3\right ] \end {align*}
✓ Solution by Maple
Time used: 0.035 (sec). Leaf size: 21
dsolve([diff(y(t),t)=-cot(t)*y(t)+6*cos(t)^2,y(1/4*Pi) = 3],y(t), singsol=all)
\[ y \relax (t ) = \frac {-2 \left (\cos ^{3}\relax (t )\right )+2 \sqrt {2}}{\sin \relax (t )} \]
✓ Solution by Mathematica
Time used: 0.063 (sec). Leaf size: 23
DSolve[{y'[t]==-Cot[t]*y[t]+6*Cos[t]^2,y[Pi/4]==3},y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 2 \sqrt {2} \csc (t)-2 \cos ^2(t) \cot (t) \\ \end{align*}