The degree of the differential equation of all curves having normal of constant length c is :

The degree of a differential equation is the highest power of the derivative in the equation.

In this case, we are dealing with curves having normal of constant length c. The normal to a curve at a particular point is the line perpendicular to the tangent to the curve at that point.

The equation of the normal to a curve y = f(x) at a point (x0, y0) is given by:

y - y0 = -1/f'(x0) * (x - x0)

where f'(x0) is the derivative of f at x0.

The length of the normal is given by the distance formula:

c = sqrt((x - x0)^2 + (y - y0)^2)

Substituting the equation of the normal into the length equation gives:

c = sqrt((x - x0)^2 + (-1/f'(x0) * (x - x0))^2)

Solving this equation for f'(x0) gives a differential equation of degree 2, because the highest power of the derivative in the equation is 2. Therefore, the degree of the differential equation of all curves having normal of constant length c is 2.