Thread: Separable Equation Problem.

Having not studied calculus for a couple of years I am a tad rusty. Was hoping someone could give me a kick start.

The question I need to solve is:

dy/dx = [(4y + 5)/(2x + 3)]^2

Any help would be much appreciated...


Regards.

Originally Posted by paulbk108

Having not studied calculus for a couple of years I am a tad rusty. Was hoping someone could give me a kick start.

The question I need to solve is:

dy/dx = [(4y + 5)/(2x + 3)]^2

Any help would be much appreciated...


Regards.

use substitutions and to solve integrals .

So is that then integration by parts?


Regards.

Originally Posted by paulbk108

So is that then integration by parts?


Regards.

No , if you make substitution you should get integral of the form :

So;

int [u^-2} = int [v^-2]

= (u^-1)/-1 = (v^-1)/-1

= [(4y + 5)^-1]/-1 = [(2x + 3)^-1]/-1 + c

Doesn't seem correct...?


Regards.

Originally Posted by paulbk108

So;

int [u^-2} = int [v^-2]

= (u^-1)/-1 = (v^-1)/-1

= [(4y + 5)^-1]/-1 = [(2x + 3)^-1]/-1 + c

Doesn't seem correct...?


Regards.

Note that : and

u = 4y + 5
=> du/dy = 4
=>dy = du/4

=> int [dy/(4y + 5^2)] = 1/4 int [du/u^2] = ...?

v = 2x + 3
=>dv/dx = 2
=>dx = dv/2

=> int [dx/(2x + 3)^2] = 1/2 int [dv/v^2] = ...?

Is that correct?


Regards.

yes , it is..