- #1
Ryumast3r
Like the title says... I should be way past this (in ODEs+Lin. Algebra). I'm just really tired, have a final tomorrow, and cannot for the life of me understand why this works out the way it does.
Here goes (and please show most steps, it'd be greatly appreciated, thanks):
Start out with:
dP/dt = - (P-5)*(P-2)
Separate dP/dT since the whole point of this is to later integrate and solve an IVP, I get all that, just don't get the transition between this :
dP/((P-5)*(P-2)) = -dt and this next part here:
(dP/3)*(1/(P-5) - 1/(P-2)) = -dt
I know it's some fractions thing all from algebra that I should know, like I said, just cannot for the life of me figure it out, I get the whole "pull dP out" thing, it's where the 3 came from that I'm having trouble with. Tried to backsolve but I think there's just some identity I'm forgetting.
Anyway, any help would be greatly appreciated. Thanks. :)
Here goes (and please show most steps, it'd be greatly appreciated, thanks):
Start out with:
dP/dt = - (P-5)*(P-2)
Separate dP/dT since the whole point of this is to later integrate and solve an IVP, I get all that, just don't get the transition between this :
dP/((P-5)*(P-2)) = -dt and this next part here:
(dP/3)*(1/(P-5) - 1/(P-2)) = -dt
I know it's some fractions thing all from algebra that I should know, like I said, just cannot for the life of me figure it out, I get the whole "pull dP out" thing, it's where the 3 came from that I'm having trouble with. Tried to backsolve but I think there's just some identity I'm forgetting.
Anyway, any help would be greatly appreciated. Thanks. :)