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# Differential Equations basics help Watch

1. It is given that dP/dt = 2P. At t = 0, P = 3.
Find the value of P when t = 2.

My working:
(Integral) (1/2P) dP = (Integral) (1) dt
So,
Ln|2P| = t + C
Let C = LnA
2P = e^(t + LnA)
2P = Ae^t

This is wrong, because apparently it is essential to leave the 2 on the side of dt and integrate it with respect to t.
Could someone please explain why you must leave the 2 on the side of dt, and how it breaks the laws of mathematics to put it on the other side?

How do you know what sides to place constants?

P = 3e^2 and P = 3e^4.

I'm sorry if this is a stupid question; this is just something I've never understood.
2. (Original post by JLegion)
It is given that dP/dt = 2P. At t = 0, P = 3.
Find the value of P when t = 2.

My working:
(Integral) (1/2P) dP = (Integral) (1) dt
So,
Ln|2P| = t + C
Let C = LnA
2P = e^(t + LnA)
2P = Ae^t

This is wrong, because apparently it is essential to leave the 2 on the side of dt and integrate it with respect to t.
Could someone please explain why you must leave the 2 on the side of dt, and how it breaks the laws of mathematics to put it on the other side?

How do you know what sides to place constants?

P = 3e^2 and P = 3e^4.

I'm sorry if this is a stupid question; this is just something I've never understood.

Integral 1/(2P) = 1/2 x integral 1/P = 1/2 x ln|P|

Moving the 2 over to the other side is irrelevant.
3. (Original post by ghostwalker)

Integral 1/(2P) = 1/2 x integral 1/P = 1/2 x ln|P|

Moving the 2 over to the other side is irrelevant.
What a ridiculous mistake.
Thank you yet again!
4. (Original post by JLegion)
What a ridiculous mistake.
Thank you yet again!
You're welcome

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