10.6.2 problem 2

Internal problem ID [1219]
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
Date solved : Monday, January 27, 2025 at 04:45:42 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {1+\cos \left (x \right )}{2-\sin \left (y\right )} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

dsolve(diff(y(x),x) = (1+cos(x))/(2-sin(y(x))),y(x), singsol=all)
 

\[ x +\sin \left (x \right )-2 y-\cos \left (y\right )+c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.326 (sec). Leaf size: 27

DSolve[D[y[x],x] == (1+Cos[x])/(2-Sin[y[x]]),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \text {InverseFunction}[-2 \text {$\#$1}-\cos (\text {$\#$1})\&][-x-\sin (x)+c_1] \]