17.8.4 problem 1.2-3 (d)

Internal problem ID [3456]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.2-3, page 12
Problem number : 1.2-3 (d)
Date solved : Monday, January 27, 2025 at 07:37:20 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=-\cot \left (t \right ) y+6 \cos \left (t \right )^{2} \end{align*}

With initial conditions

\begin{align*} y \left (\frac {\pi }{4}\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 18

dsolve([diff(y(t),t)=-cot(t)*y(t)+6*cos(t)^2,y(1/4*Pi) = 3],y(t), singsol=all)
 

\[ y = 2 \csc \left (t \right ) \left (-\cos \left (t \right )^{3}+\sqrt {2}\right ) \]

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 23

DSolve[{D[y[t],t]==-Cot[t]*y[t]+6*Cos[t]^2,y[Pi/4]==3},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to 2 \sqrt {2} \csc (t)-2 \cos ^2(t) \cot (t) \]