Internal problem ID [569]
Book: Elementary differential equations and boundary value problems, 10th ed., Boyce and
DiPrima
Section: Miscellaneous problems, end of chapter 2. Page 133
Problem number: 2.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {\cos \relax (x )+1}{2-\sin \relax (y)}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 17
dsolve(diff(y(x),x) = (1+cos(x))/(2-sin(y(x))),y(x), singsol=all)
\[ x +\sin \relax (x )-2 y \relax (x )-\cos \left (y \relax (x )\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.334 (sec). Leaf size: 27
DSolve[y'[x] == (1+Cos[x])/(2-Sin[y[x]]),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {InverseFunction}[-2 \text {$\#$1}-\cos (\text {$\#$1})\&][-x-\sin (x)+c_1] \\ \end{align*}