13.2.19 problem 23

Internal problem ID [2317]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.2. Page 9
Problem number : 23
Date solved : Monday, January 27, 2025 at 05:45:29 AM
CAS classification : [_linear]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 13

dsolve(diff(y(t),t)+tan(t)*y(t)=cos(t)*sin(t),y(t), singsol=all)
 

\[ y = \left (-\cos \left (t \right )+c_1 \right ) \cos \left (t \right ) \]

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 15

DSolve[D[y[t],t]+Tan[t]*y[t]==Cos[t]*Sin[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \cos (t) (-\cos (t)+c_1) \]