Internal problem ID [14210]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number: 52.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {\sin \left (x \right )}{\cos \left (y\right )+1}=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.187 (sec). Leaf size: 12
dsolve([diff(y(x),x)=sin(x)/(cos(y(x))+1),y(0) = 0],y(x), singsol=all)
\[ y \left (x \right ) = \operatorname {RootOf}\left (-1+\cos \left (x \right )+\textit {\_Z} +\sin \left (\textit {\_Z} \right )\right ) \]
✓ Solution by Mathematica
Time used: 0.258 (sec). Leaf size: 19
DSolve[{y'[x]==Sin[x]/(Cos[y[x]]+1),{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \text {InverseFunction}[\text {$\#$1}+\sin (\text {$\#$1})\&][1-\cos (x)] \]