Internal problem ID [14307]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.4, page 57
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\sin \left (y\right )^{2}+t \sin \left (2 y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.453 (sec). Leaf size: 21
dsolve(sin(y(t))^2+(t*sin(2*y(t)))*diff(y(t),t)=0,y(t), singsol=all)
\begin{align*} y \left (t \right ) &= \arcsin \left (\frac {1}{\sqrt {c_{1} t}}\right ) \\ y \left (t \right ) &= -\arcsin \left (\frac {1}{\sqrt {c_{1} t}}\right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 6.191 (sec). Leaf size: 26
DSolve[Sin[y[t]]^2+(t*Sin[2*y[t]])*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\begin{align*} y(t)\to 0 \\ y(t)\to \arcsin \left (\frac {e^{c_1}}{\sqrt {t}}\right ) \\ y(t)\to 0 \\ \end{align*}