Some questions on Partial differential equations
1) Find the particular solution of the differential equation given the initial condition that when and when
2) An equation resulting from plucking a string is Find
3) Given show that
4) Given show that
5) Find the rate of change of the total surface area of a right circular cone at the instant when the base radius is 5cm and the height is 12cm if the radius is increasing at 5mm/sand the height is decreasing at 15mm/s
6) In a galvanometer the deflection satisfies the differential equation :
use the laplace transforms to solve the equation for given that when
7) Determine the Fourier series for the periodic function of period defined by :
The function has a period of
8) Expand the function in a Fourier series in the range sketch the function within and outside of the given range .
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