Internal problem ID [13834]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.1, page 32
Problem number: 24.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_linear]
\[ \boxed {y^{\prime }+y \tan \left (t \right )=\sin \left (t \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 11
dsolve([diff(y(t),t)+y(t)*tan(t)=sin(t),y(0) = 0],y(t), singsol=all)
\[ y = -\cos \left (t \right ) \ln \left (\cos \left (t \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.054 (sec). Leaf size: 12
DSolve[{y'[t]+y[t]*Tan[t]==Sin[t],{y[0]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\cos (t) \log (\cos (t)) \]