a) Find the partial differential equation of all spheres whose centre…

Previous year question for Engineering Mathematics-II.

Question

a) Find the partial differential equation of all spheres whose centres lies on the z-axis.

b) Solve: $y^2(x-y)p + x^2(y-x)q = (x^2+y^2)z$.

c) Solve: $p^3 + q^3 = 3pqz$.

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