• 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