76.1.27 problem 27

Internal problem ID [17326]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.1 (Separable equations). Problems at page 44
Problem number : 27
Date solved : Tuesday, January 28, 2025 at 10:00:23 AM
CAS classification : [_separable]

\begin{align*} \sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (\frac {\pi }{2}\right )&=\frac {\pi }{3} \end{align*}

✓ Solution by Maple

Time used: 0.235 (sec). Leaf size: 19

dsolve([sin(2*x)+cos(3*y(x))*diff(y(x),x)=0,y(1/2*Pi) = 1/3*Pi],y(x), singsol=all)
 

\[ y = -\frac {\arcsin \left (\frac {3}{2}+\frac {3 \cos \left (2 x \right )}{2}\right )}{3}+\frac {\pi }{3} \]

✗ Solution by Mathematica

Time used: 0.000 (sec). Leaf size: 0

DSolve[{Sin[2*x]+Cos[3*y[x]]*D[y[x],x]==0,{y[Pi/2]==Pi/3}},y[x],x,IncludeSingularSolutions -> True]
 

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