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I want to solve an equation. I want to get all steps for the solution with details and explnation.
Ψ(r, y, t) = (Rr)1/2/2ΠK{(2-k2) K(k)-2E(k)} - (Rr)1/2/2ΠK {(2 - k2) K(k-) - 2E(k-)},
where
k2 = 4Rr/(y - Y)2 + (r + R)2, k-2 = 4Rr/(y + Y)2 + (r + R)2'
Where K and E are complete elliptic integrals of the first and second kind.
K(k) = 0∫1/2Π(1 - k2 sin2 dx)-1/2dx, E(k) = 0∫1/2Π(1 - k2 sin2x)1/2 dx.
Ur = (1/r * ∂Ψ/∂y)
Uy = (-1/r * ∂Ψ/∂y)
∂Φ/∂r = Ur
∂Φ/∂y = Uy
∂Φ/∂y = Uy = 0 at y = 0
I want to find (Φ). After that find the constant which include with equation after integral.
Differentiated Φ with respect to y and apply
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