Internal problem ID [7928]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 348.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {\left (x \cos \relax (y)+\sin \relax (x )\right ) y^{\prime }+y \cos \relax (x )+\sin \relax (y)=0} \end {gather*}
✓ Solution by Maple
Time used: 0.062 (sec). Leaf size: 15
dsolve((x*cos(y(x))+sin(x))*diff(y(x),x)+y(x)*cos(x)+sin(y(x)) = 0,y(x), singsol=all)
\[ y \relax (x ) \sin \relax (x )+\sin \left (y \relax (x )\right ) x +c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.126 (sec). Leaf size: 17
DSolve[Sin[y[x]] + Cos[x]*y[x] + (x*Cos[y[x]] + Sin[x])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}[x \sin (y(x))+y(x) \sin (x)=c_1,y(x)] \]