Question

Find the equation of the curve whose slope, at any point (x, y), is
y/x^2 and which satisfies the
condition y = 1 when x = 3.​

Answer 1

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(dy/dx) = —y

(dy/y) = —dx

Integrating on both sides.

∫(dy/y) = —∫dx

log(y) = —x + logC where logC is a constant.

logC — log(y) = x

log(C/y) = x

C/y = eˣ

yeˣ = C

Since this curve passes through (2,1)

Therefore point (2,1) will satisfy the obtained curve.

1e² = C

C = e²

Putting this value of C in the above obtained curve.

Answer : yeˣ = e²

I hope my answer helps you....✌

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