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Partial Differential Equations : Linear and Non-Linear, Order and Dependent and Independent Variables

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A) Solve the equation uxy = x^2 y and its particular solution fur which u(1,y)= cos(y).
b) Determine whether each of the following partial differential equations is linear or nonlinear, state the order of the equation, and name the dependent and independent variables.
i) ut=9uyy
ii) x^2Pzz = z^2Pxx
iii) WWrr=pqr
iv) sxx + syy +szz =0
v) (xu)^2 + (xy)^2 = 10

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PDEs, linear and non-linear, order and dependent and independent variables are investigated. The solution is detailed and well presented.

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(a)
Write as . Multiply both sides by dx.

Integrate both sides:

Instead of getting a constant of integration, all we know is that we have something that is constant with respect to y, which means some (at this point unknown) function of y. Now multiply both sides by dy - same trick as above with x - don't worry about the difference between  and d !

Integrate both ...

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