Internal problem ID [13122]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 8. Review exercises for part of part II. page 143
Problem number: 20.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {\sin \left (y\right )+\left (x +1\right ) \cos \left (y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 14
dsolve(sin(y(x))+(1+x)*cos(y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \arcsin \left (\frac {1}{c_{1} \left (1+x \right )}\right ) \]
✓ Solution by Mathematica
Time used: 19.016 (sec). Leaf size: 21
DSolve[Sin[y[x]]+(1+x)*Cos[y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \arcsin \left (\frac {e^{c_1}}{x+1}\right ) y(x)\to 0 \end{align*}