Question

Consider the function Let

$z(x,y) = e^y f(ye^{\frac{x^2}{2y^2}}) , (x,y)\epsilon R^2 \setminus \left \{ (t,0) | t \epsilon R \right \}$

where f(t) is differentiable for all t ∈ R. Show that z satisfies the partial differential equation

(x² − y² ) ∂z/∂x + xy ∂z/∂y = xyz

for all (x, y) ∈ R² \ { (t, 0)|t ∈ R }.

Answer 1

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