10.2.19 problem 19

Internal problem ID [1147]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.2. Page 48
Problem number : 19
Date solved : Monday, January 27, 2025 at 04:35:53 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 )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.083 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.487 (sec). Leaf size: 16

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

\[ y(x)\to \frac {1}{3} \arcsin \left (3 \cos ^2(x)\right ) \]