Find the equation of the curve which passes through the point (2, 2) and satisfies the differential equation

Question

Philoid · Accepted Answer

Given the differential equation

⇒

Integrating both sides we have,

⇒

⇒ log|y| + log|1 – y| = log|1 + x| + logc

⇒ log|y(1 – y)| = log|c(1 + x)|

⇒ y(1 – y) = c(1 + x) ……(1)

Since, the equation passes through (2,2), So,

2(1 – 2) = c(1 + 2)

⇒ – 2 = c×3

⇒ c =

Therefore, equation (1) becomes

y(1 – y) = (1 + x)