Internal problem ID [13121]
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: 19.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact, [_1st_order, `_with_symmetry_[F(x)*G(y),0]`]]
\[ \boxed {\sin \left (y\right )+\left (x +y\right ) \cos \left (y\right ) y^{\prime }=0} \]
✓ Solution by Maple
Time used: 0.079 (sec). Leaf size: 26
dsolve(sin(y(x))+(x+y(x))*cos(y(x))*diff(y(x),x)=0,y(x), singsol=all)
\[ x -\frac {-\cos \left (y \left (x \right )\right )-\sin \left (y \left (x \right )\right ) y \left (x \right )+c_{1}}{\sin \left (y \left (x \right )\right )} = 0 \]
✓ Solution by Mathematica
Time used: 0.193 (sec). Leaf size: 29
DSolve[Sin[y[x]]+(x+y[x])*Cos[y[x]]*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}[x=\csc (y(x)) (-y(x) \sin (y(x))-\cos (y(x)))+c_1 \csc (y(x)),y(x)] \]