maths - solving differential equations

when solving a differential equation, how do you know which side to put a constant on?

eg.
dp/dt =kp

I did ∫1/kp dp = ∫dt but the mark scheme says its ∫1/p dp = ∫ k dt

another question was
dh/dt=0.4-k√h

I did ∫k√h dh = ∫ 0.4 dt
but the mark scheme said ∫1/0.4-k√h dh = ∫dt

Reply 1

CaptainDuckie

Study Forum Helper

Get the common variables on one side :yy:

(edited 2 years ago)

Reply 2

JGLM

So the first one should be fine either way, the constant can be either side, the issue with the second one is that you have k.rt(h) + dh/dt = 0.4, which when integrated gives ∫k.rt(h)dt + ∫dh = ∫0.4dt.

It has to be written in the form f(h)dh/dt=f(t) to be integrable by the variable separable method.

Reply 3

libbyab

Original post by JGLM

oh I see thank you, so if theres no addition or subtraction involved, it doesn't matter which side the constant is on?

Reply 4

JGLM

Original post by libbyab

oh I see thank you, so if theres no addition or subtraction involved, it doesn't matter which side the constant is on?

Well I suppose that’s one way of putting it. As long as your algebra is correct, the constant can go wherever it likes, but you have to be careful to integrate with the right variables, you can’t integrate h with respect to t.