74.1.25 problem 32

Internal problem ID [15805]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 1. Introduction to Differential Equations. Exercises 1.1, page 10
Problem number : 32
Date solved : Tuesday, January 28, 2025 at 08:07:51 AM
CAS classification : [_exact, [_1st_order, `_with_symmetry_[F(x),G(y)]`], [_Abel, `2nd type`, `class A`]]

\begin{align*} y \cos \left (t \right )+\left (2 y+\sin \left (t \right )\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 41

dsolve(y(t)*cos(t)+(2*y(t)+sin(t))*diff(y(t),t)=0,y(t), singsol=all)
 

\begin{align*} y &= -\frac {\sin \left (t \right )}{2}-\frac {\sqrt {\sin \left (t \right )^{2}-4 c_{1}}}{2} \\ y &= -\frac {\sin \left (t \right )}{2}+\frac {\sqrt {\sin \left (t \right )^{2}-4 c_{1}}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.175 (sec). Leaf size: 60

DSolve[y[t]*Cos[t]+(2*y[t]+Sin[t])*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\begin{align*} y(t)\to \frac {1}{2} \left (-\sin (t)-\sqrt {\sin ^2(t)+4 c_1}\right ) \\ y(t)\to \frac {1}{2} \left (-\sin (t)+\sqrt {\sin ^2(t)+4 c_1}\right ) \\ y(t)\to 0 \\ \end{align*}