• 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