Open Question: anyone please answer this for me dy/dt=ky ln 200/y?

dy/dt = k * y * ln(200 / y)
dy / (y * ln(200 / y)) = k * dt
dy / (y * (ln(200) - ln(y))) = k * dt

u = ln(200) - ln(y))
du = -dy / y

-du / u = k * dt

Integrate

-ln|u| = kt + C
ln|u| = -(kt + C)
u = e^(-kt + C)
ln(200 / y) = e^(-(kt + C))

ln(200 / 20) = e^(-C)
ln(10) = e^(-C)
1 / ln(10) = e^(C)
-ln(ln(10)) = C

ln(200 / y) = e^(-(kt - ln(ln(10))))
ln(200 / y) = e^(ln(ln(10)) - kt)
ln(200 / y) = ln(10) * e^(-kt)

ln(200 / 48) = ln(10) * e^(-3k)
ln(25/6) = ln(10) * e^(-3k)
e^(3k) = ln(10) / ln(25/6)
3k = ln(ln(10) / ln(25/6))
k = (1/3) * ln(ln(10) / ln(25/6))

ln(200 / y) = ln(10) * e^((-1/3) * ln(ln(10) / ln(25/6)) * t)
ln(200 / y) = ln(10) * (ln(10) / ln(25/6)) * e^(-t/3)
ln(200 / y) = ln(10)^2 * e^(-t/3) / ln(25/6)

t = 15

ln(200 / y) = ln(10)^2 * e^(-5) / ln(25/6)
200 / y = e^(ln(10)^2 * e^(-5) / ln(25/6))
y / 200 = 1 / e^(ln(10) * ln(10) * e^(-5) / ln(25/6))
y = 200 / e^(ln(10)^2 / (e^(5) * ln(25/6)))
y = 195.05569516562951956450191705787

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