# Solve the differential equation #dy/dt = 4 sqrt(yt)# y(1)=6?

and:

This is separable.

Differentiate both sides wrt t:

Chain rules allows us to re-write first term:

Then integrate:

So:

And:

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Integrating both sides and rewriting with fractional exponents:

Using typical integration rules:

Then:

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The solution to the given differential equation ( \frac{dy}{dt} = 4\sqrt{yt} ) with the initial condition ( y(1) = 6 ) is ( y(t) = (t^2 + 1)^2 ).

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