Texts:
Q3a: Express the following function as a unit step function and hence find its Laplace Transform:
0, 0 < t < 1, ft = {2t, 1 < t < 2}
(b) Find the singular solution of the Clairaut's equation az z = px + qy + p^2 - q
Total: 20 Marks
Q4(a): Using Parseval's theorem, deduce the series TE where the Euler-Fourier coefficients of y = x over -T, T with period 2T are obtained as 2n^2 - 1 and bn = 0.
Total: 12 Marks
(b) Find the complete solution of the following differential equation: p + q = x - y
Total: 20 Marks
Q5(a): Find the particular solution of dt
(b) Find the inverse Laplace transform of 1 / (s^2 + s^2 + 4)
(c) Find the complete solution of the partial differential equation p + q = pq
Total: 20 Marks
