functions

Show that if f = f(x,y) and fyy = 0, then f(x,y) = g(x)y + h(x) for some functions g, h.
(Start by stating the form taken by fy.)

There is nothing in our notes to suggest what the significance of fyy=0 has, and even so I don't know where to start. Help please?

Quote:

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Originally Posted by algebra123

Show that if f = f(x,y) and fyy = 0, then f(x,y) = g(x)y + h(x) for some functions g, h.
(Start by stating the form taken by fy.)

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If then it is clear that for some .

Hence for some .
Here 'acts' as the constant in the indefinite anti-derivative.