Form the differential equation corresponding to `y=cx-2c^(2)`, where c is a parameter.

Find the order of the differential equation corresponding to y=c(x-c)^(2) , where c is an arbitrary constant.

Find the order of the differential equation corresponding to (i) y = c(x-c)^(2) where c is an arbitrary constant. (ii) y = Ae^(x) + Be^(3x) + Ce^(5x) where A, B, C are arbitrary constant. (iii) xy = c e^(x) + b e^(-x) + x^(2) where b, c are arbitrary constants. (iv) The family of all circles in the xy-plane with centre at the origin.

Form the D.E corresponding to y = cx-2c^2 where c is a parameter.

Form the differential equation corresponding to y=A cos 3x+B sin 3x, where A and B are parameters.

Find the differential equation corresponding to xy=ae^(x)+be^(-x) , and an b are parameters.

Form the differential equations the family of curves y = cx + c - c^(2) where c is a parameter.

Form the differential equation corresponding to the family of circles of radius r given by (x-a)^(2)+(y-b)^(2)=r^(2) , where a and b are parameters.

The differential equation whose solution is y = ce^(-2x) , where c is an arbitrary constant, is

Form the differential equation corresponding to the family of circles passing through the origin and having centres on Y-axis.

Find the order of the differential equation corresponding to y=Ae^(x)+Be^(3x)+Ce^(5x) (A, B, C being parameters) is a solution.