74.4.52 problem 52

Internal problem ID [15945]
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
Date solved : Tuesday, January 28, 2025 at 08:24:08 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.251 (sec). Leaf size: 12

dsolve([diff(y(x),x)=sin(x)/(cos(y(x))+1),y(0) = 0],y(x), singsol=all)
 

\[ y = \operatorname {RootOf}\left (-1+\cos \left (x \right )+\sin \left (\textit {\_Z} \right )+\textit {\_Z} \right ) \]

✓ Solution by Mathematica

Time used: 0.244 (sec). Leaf size: 19

DSolve[{D[y[x],x]==Sin[x]/(Cos[y[x]]+1),{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

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