Question

Dy/dt = y^2

y(t) = ?

Answer 1

`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)`