Consider a two-dimensional circular metal plate of radius R and let u be its temperature distribution. Suppose that the initial temperature is an arbitrary function f. Using the method of separation of variables and assuming that the separation constant is non-positive, that is -k?, where k 2 0, derive the general solution to the problem in situations where we have radial symmetry and the circumference of the plate is insulated. [You need not find the expression for the norm ||/o|| that would appear in the formula for the Fourier-Bessel coefficients.]

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.