Form the differential equations of the following families of curves by elimnating the parameters (arbitrary constants) given against them in the brackets.
(i) `y = c(x-c)^(2), (c)`
(ii) `xy = a e^(x) + b e^(-x), (a, b)`
(iii) `y = (a+bx)e^(Kx), (a,b)`
(iv) `y = a cos (nx + b), (a,b)`
(v) = `y = a e^(3x) + be^(4x), (a,b)`
(vi) `y = ax^(2) + bx, (a,b)`
(vii) `ax^(2) + by^(2) = 1` (a,b)

Answer

(i) `((dy)/(dx))^(3) - 4xy(dy)/(dx) + 8y^(2) = 0`
(ii) `x(d^(2)y)/(dx^(2)) + 2(dy)/(dx) - xy = 0`
(iii) `y_(2) - 2ky_(1) + k^(2)y = 0`
(iv) `y_(2) + n^(2)y = 0`
(v) `y_(2) - 7y_(1) + 12y = 0`
(vi) `x^(2)(d^(2)y)/(dx^(2)) - 2x(dy)/(dx) + 2y = 0`
(vii) `xy y_(2) + xy_(1)^(2) - y y_(1) = 0`