Answer to Question #58208 in Physics for Nayan Jyoti Das

Question

5. a) Classify the following PDEs by way of order and degree, linearity/nonlinearity,
homogeneity/non-homogeneity:

i) d^2 u / dt^2 = d^2 u / dx^2 + x

ii) [1- (du/dt)^2] d^2 u / dx^2 - [1+ (du/dx)^2] d^2 u / dt^2 = 0

5. b) Show that the function f (x, y) = a(x^2 − y^2 ) + bxy where a and b are constants, is a solution of Laplace’s equation.

5. c) Obtain all the first and second order partial derivatives of the function:

f(x,y) = y e^x - x^2 - y^-2 + tan y