Internal problem ID [497]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Section 2.2. Page 48
Problem number: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\sin \left (2 x \right )+\cos \left (3 y\right ) y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} \left [y \left (\frac {\pi }{2}\right ) = 0\right ] \end {align*}
✓ Solution by Maple
Time used: 0.078 (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)
\[ y \relax (x ) = \frac {\arcsin \left (\frac {3}{2}+\frac {3 \cos \left (2 x \right )}{2}\right )}{3} \]
✓ Solution by Mathematica
Time used: 0.515 (sec). Leaf size: 16
DSolve[{Sin[2*x]+Cos[3*y[x]]*y'[x] == 0,y[Pi/2]==0},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{3} \text {ArcSin}\left (3 \cos ^2(x)\right ) \\ \end{align*}