Question

Dy/dt = y^2

y(t) = ?

Answer 1

`y(t)=-(1)/(t+C)`

Explanation:

We are given that

`(dy)/(dt)=y^2`

We have to find the value of y(t).

`(dy)/(dt)=y^2`

`(dy)/(y^2)=dt`

Integrating on both sides

`\int y^(-2)dy=\int dt`

We know that
`\int x^n dx=(x^(n+1))/(n+1)+C`

Using the formula

`(y^(-1))/(-1)=t+C`

`-(1)/(y)=t+C`

`a^(-1)=(1)/(a)`

Taking the reciprocal on both side then , we get

`-y=(1)/(t+C)`

`y(t)=-(1)/(t+C)`