74.6.18 problem 19

Internal problem ID [16041]
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
Date solved : Tuesday, January 28, 2025 at 08:28:46 AM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.998 (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 &= \arcsin \left (\frac {1}{\sqrt {c_{1} t}}\right ) \\ y &= -\arcsin \left (\frac {1}{\sqrt {c_{1} t}}\right ) \\ \end{align*}

✓ Solution by Mathematica

Time used: 5.809 (sec). Leaf size: 26

DSolve[Sin[y[t]]^2+(t*Sin[2*y[t]])*D[y[t],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*}