Angabe:

Man löse die homogenen Differentialgleichungen!

(xsin y/x - ycos y/x)dx + xcos y/x dy = 0

Lösung:

Substitution: y/x = z => y = zx

dy = xdz + zdx

xsinz - zxcoszdx + zxcoszdx = -x^2 * coszdz
xsinzdx = -x^2 coszdz
1/x dx = -cosz/sinz dz

Int...Integral

Int 1/x dx = Int - cosz/sinz dz
ln|x| = -ln|sinz| + c
ln|x| = -ln|sin y/x| + c