Question

Find the solution of the differential equation that satisfies the given initial condition.

dP/dt=4 square root (Pt), P(1)=2

Answer 1

Is your equation this:
\[ \frac{dP}{dt} = 4\sqrt{P(t)} \]
?

Answer 2

sqrt(P(t))-2*t-_C1 = 0

Answer 3

We'd never leave a function in that form ... and you should also show the derivation ;-)

Answer 4

well plug in initial condition and stuff

Answer 5

For the record then: write P for P(t). Then the equation we have is
\[ \frac{dP}{dt} = 4\sqrt{P} \]
Separating variables,
\[ \int \frac{dP}{\sqrt{P}} = \int 4 \ dt \]
Now integrating we have
\[ \frac{1}{2} \sqrt{P} = 4t + C \]
or
\[ P(t) = (8t + 2C)^2 \]
You can now apply the initial condition \( P(1) = 2 \) to simplify this further by solving for \( C \).

Answer 6

**correction, upon integrating we have
\[ 2 \sqrt{P} = 4t + C \]
and thus
\[ \sqrt{P} = 2t + C/2 \]
\[ P(t) = (2t + C/2)^2 \]