Answer to Question #203899 in Electrical Engineering for Bahawal Tahir

Question #203899

(a) Find fx(x,y), fy(x,y), fx(1,3), and fy(-2,4) for the given function. If 

𝑧 = 𝑓(𝑥, 𝑦) = 3𝑥

ଷ𝑦

ଶ − 𝑥

ଶ𝑦

ଷ + 4𝑥 + 9


1
Expert's answer
2021-06-08T22:26:01-0400

Given a constant k ∈ R, find all solutions f : R → R to the differential equation

"f '(x) = k f (x)"

Multiply the equation above "f '(x) \u2212 kf (x) = 0\\space by \\space e^{\u2212kx}"

"f '(x) e^{\u2212kx }\u2212 f (x) ke^{\u2212kx} = 0."

The left-hand side is a total derivative,"[f (x) e^{\u2212kx}0] = 0."

The solution of the equation above is"f (x)e\u2212kx = c, with c \u2208 R.\nTherefore, f (x) = c ekx."


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