# Math Help - Differential Equations

1. ## Differential Equations

Can anyone help me solve the following differential equation that satisfies the given initial condition?

dP/dt=4(sqrt of Pt)

where P(1) =7

When I did it, I got P=(1/12p^3/2 + sqrt of 7 - 1/2)^2.

Can anyone figure out what i'm doing wrong?? Thanks.

2. Originally Posted by Jessica098
Can anyone help me solve the following differential equation that satisfies the given initial condition?

dP/dt=4(sqrt of Pt)

where P(1) =7

When I did it, I got P=(1/12p^3/2 + sqrt of 7 - 1/2)^2.

Can anyone figure out what i'm doing wrong?? Thanks.
I think what you have is this

$\frac{dP}{dt}=4\sqrt{Pt}=4\sqrt{P}\sqrt{t}$

Now seperating variables we get

$\frac{dP}{\sqrt{P}}=4\sqrt{t}dt$

remaining equality we see that

$\int\frac{dP}{\sqrt{P}}=\int{4\sqrt{t}}dt\Rightarr ow{2\sqrt{P}=\frac{8}{3}t^{\frac{3}{2}}+C}$

Solving for P we get

$P=\bigg(\frac{4}{3}t^{\frac{3}{2}}+C\bigg)^2$

Can you go from there?