dj_m.o.h.t.
12-06-2002, 20:43
Angabe:
Man löse die exakten Differentialgleichungen!
(cosy + ycosx)dx + (sinx - xsiny)dy = 0
Lösung:
cosy + ycosx = P
sinx - xsiny = Q
dP/dy = -siny + cosx
dQ/dx = cosx - siny
Int...Integral
Int Pdx + Int Q - Int dP/dy dxdy=0
Int cosy + ycosx dx + Int sinx - xsiny - Int cosx - siny dxdy = c
xcosy + ysinx + ysinx + xcosy - ysinx - xcosy = c
ysinx + xcosy = c
Man löse die exakten Differentialgleichungen!
(cosy + ycosx)dx + (sinx - xsiny)dy = 0
Lösung:
cosy + ycosx = P
sinx - xsiny = Q
dP/dy = -siny + cosx
dQ/dx = cosx - siny
Int...Integral
Int Pdx + Int Q - Int dP/dy dxdy=0
Int cosy + ycosx dx + Int sinx - xsiny - Int cosx - siny dxdy = c
xcosy + ysinx + ysinx + xcosy - ysinx - xcosy = c
ysinx + xcosy = c