Internal problem ID [14069]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type
[_exact, [_1st_order, `_with_symmetry_[F(x),G(y)]`], [_Abel, `2nd type`, `class A`]]
\[ \boxed {\cos \left (t \right ) y+\left (2 y+\sin \left (t \right )\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.0 (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 \left (t \right ) &= -\frac {\sin \left (t \right )}{2}-\frac {\sqrt {\sin \left (t \right )^{2}-4 c_{1}}}{2} \\ y \left (t \right ) &= -\frac {\sin \left (t \right )}{2}+\frac {\sqrt {\sin \left (t \right )^{2}-4 c_{1}}}{2} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.151 (sec). Leaf size: 60
DSolve[y[t]*Cos[t]+(2*y[t]+Sin[t])*y'[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*}