Internal problem ID [7935]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 355.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {\left (x \cos \relax (y)+\cos \relax (x )\right ) y^{\prime }-y \sin \relax (x )+\sin \relax (y)=0} \end {gather*}
✓ Solution by Maple
Time used: 0.028 (sec). Leaf size: 15
dsolve((x*cos(y(x))+cos(x))*diff(y(x),x)-y(x)*sin(x)+sin(y(x)) = 0,y(x), singsol=all)
\[ y \relax (x ) \cos \relax (x )+x \sin \left (y \relax (x )\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.134 (sec). Leaf size: 17
DSolve[Sin[y[x]] - Sin[x]*y[x] + (Cos[x] + x*Cos[y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}[x \sin (y(x))+y(x) \cos (x)=c_1,y(x)] \]