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Dy/dt = y^2

y(t) = ?

User Ziaul
by
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1 Answer

2 votes

Answer:


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)

User Bronanaza
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