Internal problem ID [7941]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 361.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
Solve \begin {gather*} \boxed {\left (x \sin \left (y x \right )+\cos \left (x +y\right )-\sin \relax (y)\right ) y^{\prime }+y \sin \left (y x \right )+\cos \left (x +y\right )+\cos \relax (x )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.063 (sec). Leaf size: 22
dsolve((x*sin(x*y(x))+cos(x+y(x))-sin(y(x)))*diff(y(x),x)+y(x)*sin(x*y(x))+cos(x+y(x))+cos(x) = 0,y(x), singsol=all)
\[ -\cos \left (x y \relax (x )\right )+\sin \relax (x )+\sin \left (y \relax (x )+x \right )+\cos \left (y \relax (x )\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.567 (sec). Leaf size: 31
DSolve[Cos[x] + Cos[x + y[x]] + Sin[x*y[x]]*y[x] + (Cos[x + y[x]] - Sin[y[x]] + x*Sin[x*y[x]])*y'[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ \text {Solve}[\cos (y(x))-\cos (x y(x))+\sin (x) \cos (y(x))+\cos (x) \sin (y(x))+\sin (x)=c_1,y(x)] \]