General solution of diffential equation

[delsoo]

Homework Statement

for this question , i dun know which method should i use... can someone enlighten me on this? i sub y=vx then differentiate with respect to x but can't get the ans

Homework Equations

The Attempt at a Solution

 

[Simon Bridge]

Please show your working.
Have you identified what sort of DE it is?

edit: it says "solve this equation and hence find the general solution of the DE..." with the DE following; which seems to imply there is an equation just above the start of the question that you solve first.

 

[delsoo]

Please show your working.
Have you identified what sort of DE it is?

edit: it says "solve this equation and hence find the general solution of the DE..." with the DE following; which seems to imply there is an equation just above the start of the question that you solve first.

i am not sure what type of de it is

 

[Simon Bridge]

You need to be able to classify differential equations - it will help you locate strategies and talk to people about them. You will have notes on the names of DEs in your coursework.

Do you know the order of the DE at least?

Anyway:

I take it you are doing "substitution" methods in your course right now - is that correct?
The key to substitution method is to look for something that is f(x/y) or f(xy) and put v=<the thing inside the function>

In this case, try v=xy and compare your DE with xv'.

The idea is to end up with a separable equation.

 

[BiGyElLoWhAt]

Doesn't he have one to begin with?

 

[Simon Bridge]

Doesn't he have one to begin with?

... a separable DE? Well, let's see:
The differential equation to be solved is:$$x^2\frac{dy}{dx}=1-2(xy)^2$$ ... how would you attempt to separate that?

(Note: I wrote it that way so OP may be able to see why v=xy may be a good thing to try.)

 

[delsoo]

u mean i should try v=xy? for this case?

 

[Simon Bridge]

[Do yo]u mean [that I] should try v=xy for this case?

... See post #4:

In this case, try v=xy and compare your DE with xv'.

... can you see why this is a likely thing to try?

Aside: Please try to write literate sentences - why should anyone be bothered to help you when you cannot be bothered to type an extra couple of letters.