🏫 National Institute of Technology Silchar

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S No	Questions	Marks	CO
1.	Obtain the half-range Fourier sine series expansion of the function shown in the figure below: y = f(x) A triangular wave with peak at k occurring at L/2, starting from 0 and ending at L on the x-axis.	5	CO-2
2.	Find the Fourier cosine transform of e-x².	5	CO-2
3.	Form a partial differential equation by eliminating the arbitrary function F from the relation F(x² + y², x² - z²) = 0.	5	CO-1
4.	Obtain the general solution of x(y² + z)(∂z/∂x) - y(x² + z)(∂z/∂y) = (x² - y²)z.	5	CO-1
5.	Find a complete integral of z² = xy(∂z/∂x)(∂z/∂y).	5	CO-1
6.	Obtain the general solution of the following PDE ∂²z/∂x² - 6(∂²z/∂x∂y) + 9(∂²z/∂y²) -4(∂z/∂x)+ 12(∂z/∂y) + 4z = 2e2xsin(y + 3x).	5	CO-1