dj_m.o.h.t.
12-06-2002, 20:31
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
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