Question

dy/dt = y^2

y(t) = ?

Answer 1

Answer:

$y(t) = \displaystyle\frac{-1}{t + c}$  

Step-by-step explanation:

$\frac{dy}{dt} = y^2$

$\frac{dy}{y^2} = dt$

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

Integrating, both sides, we get

$\displaystyle\int \displaystyle\frac{dy}{y^2}= \int dt$

$\displaystyle\frac{y^{-1}}{-1} = t + c$

where, c is the integration constant.

$\displaystyle\frac{-1}{y} = t + c$

$y = \displaystyle\frac{-1}{t + c}$

Thus, the obtained y(t) is

$y(t) = \displaystyle\frac{-1}{t + c}$