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For the harmonic potential V(x,y) = x^2 + y^2

a) Find the total differential, dV.
For this I got dV = 2x.dx + 2y.dy

b) Given that -dV = F(x).dx + F(y).dy, where F(x) and F(y) is the force in the x and y direction, respectively, write a differential equation describing the change of potential energy, V(x), with position x.

I am really not sure about this. Should I integrate the whole equation and then differentiate with respect to x?

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