Internal problem ID [4582]
Book: Engineering Mathematics. By K. A. Stroud. 5th edition. Industrial press Inc. NY.
2001
Section: Program 24. First order differential equations. Further problems 24. page 1068
Problem number: 4.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {\cos \relax (y)+\left (1+{\mathrm e}^{-x}\right ) \sin \relax (y) y^{\prime }=0} \end {gather*} With initial conditions \begin {align*} \left [y \relax (0) = \frac {\pi }{4}\right ] \end {align*}
✓ Solution by Maple
Time used: 0.404 (sec). Leaf size: 14
dsolve([cos(y(x))+(1+exp(-x))*sin(y(x))*diff(y(x),x)=0,y(0) = 1/4*Pi],y(x), singsol=all)
\[ y \relax (x ) = \arccos \left (\frac {\sqrt {2}\, \left ({\mathrm e}^{x}+1\right )}{4}\right ) \]
✓ Solution by Mathematica
Time used: 5.452 (sec). Leaf size: 20
DSolve[{Cos[y[x]]+(1+Exp[-x])*Sin[y[x]]*y'[x]==0,{y[0]==Pi/4}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \text {ArcCos}\left (\frac {e^x+1}{2 \sqrt {2}}\right ) \\ \end{align*}