Dy/dt = y^2 y(t) = ?

Question

asked Feb 14, 2020 13.9k views

1 Answer

Thatdankent · Answer 1 · 2020-02-18T23:34:00+0000

Answer:

$y(t) = \displaystyle(-1)/(t + c)$

Explanation:

(dy)/(dt) = y^2

(dy)/(y^2) = dt

If we integrate both the sides, we can get y(t)

Integrating, both sides, we get

$\displaystyle\int \displaystyle(dy)/(y^2)= \int dt$

$\displaystyle(y^(-1))/(-1) = t + c$

where, c is the integration constant.

$\displaystyle(-1)/(y) = t + c$

$y = \displaystyle(-1)/(t + c)$

Thus, the obtained y(t) is

$y(t) = \displaystyle(-1)/(t + c)$