Question

If y = (ax + b)/(Ax + B)  and z = (ay + b)/(Ay + B), prove that y"'/y'   – 3/2(y"/y')² = 0 = z"'/z'   – 3/2( z"/z')²

Answer 1

 Given y = (ax + b)/(Ax + B)

(Ax + B)y = ax + b

Differentiating w.r.t x, we get,

(Ax + B)y' + Ay = a ...(i)

(Ax + B)y" + 2Ay' = 0 ...(ii)

(Ax + B)y"' + 3Ay" = 0 ...(iii)

Dividing (iii) by (ii), we get,

which is same as of the form y = (ax + b)/(Ax + B)

So, we can easily prove that