Internal problem ID [3146]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 2. First-Order and Simple Higher-Order Differential Equations. Page
78
Problem number: 1.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\cos \left (y\right )^{2}+\left (1+{\mathrm e}^{-x}\right ) \sin \left (y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 18
dsolve(cos(y(x))^2+(1+exp(-x))*sin(y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\pi }{2}+\arcsin \left (\frac {1}{\ln \left (1+{\mathrm e}^{x}\right )+c_{1}}\right ) \]
✓ Solution by Mathematica
Time used: 0.95 (sec). Leaf size: 57
DSolve[Cos[y[x]]^2+(1+Exp[-x])*Sin[y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\sec ^{-1}\left (-\log \left (e^x+1\right )+2 c_1\right ) \\ y(x)\to \sec ^{-1}\left (-\log \left (e^x+1\right )+2 c_1\right ) \\ y(x)\to -\frac {\pi }{2} \\ y(x)\to \frac {\pi }{2} \\ \end{align*}