Some questions on Partial differential equations 1) Fin

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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