Separating Variables

[actuary-to-be]

Hi guys.. very basic question

Suppose we have the following differential equation
d/dt p(t) = - p(t) * m(x+t)

we can use separation of variables to solve it and get an expression for m(x+t), right?

so dividing both sides by p(t), we get
[d/dt p(t)]/p(t) = - m(x+t)

how do I simplify the left hand side of this?
in the notes it says it should be
d/dt ln(p(t)) = -m(x+t)

but I don't quite understand how we got the ln(p(t)) there...

anyone know?

thank you

 

[deepakraomore]

To solve the separated variables we need to integrate the equations wrt to separated variable. So integrating d/dt ln(p(t)) = ln(p(t)).

 

[actuary-to-be]

Ah thank you. makes sense