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+1 vote
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in Differential Equations by (50.2k points)
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Find the equation of a curve passing through (2, 1) if the slope of the tangent to the curve at any point (x, y) is (x2 + y2)/2xy.

1 Answer

+1 vote
by (48.8k points)
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Best answer

Differentiate vx using product rule,

Put 1 – v2 = t hence differentiating with respect to v we get dt/dv = -2v which means 2vdv = -dt

Now it is given that the curve is passing through (2, 1)

Hence (2, 1) will satisfy the curve equation (a)

Putting values x = 2 and y = 1 in (a)

Put c in equation (a)

Using log a + log b = log ab

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