Question: Show that the function u = p(ry) + VTy v(y/r) provides the equation Pu = 0.

Show that the function u = p(ry) + VTy v(y/r) provides the

Show that the function u = p(ry) + VTy v(y/r) provides the equation Pu = 0.

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To show that the given function u varphixy sqrtfracyx psileftfracyx ight satisfies the equation x2 fracpartial2 upartial x2 y2 fracpartial2 upartial y2 0 we will need to calculate the partial derivatives and verify the equation Step 1 Calculate the First Partial Derivatives 1 With respect to x u varphixy sqrtfracyx psileftfracyx ight Let z xy and w fracyx so u varphiz sqrtw psiw By the chain rule the partial derivative of u with respect to x is fracpartial upartial x yvarphixy frac12 sqrtfracyx3 psileftfracyx ight sqrtfracyx psileftfracyx ight leftfracyx2 ight 2 With respect to y The partial derivative of u with respect to y is fracpartial upartial y ... View full answer

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