# Integrating factor

1. Feb 15, 2016

### goldfish9776

1. The problem statement, all variables and given/known data
is my integral R(x) and R(y) correct ? why it look so complicated ?
2. Relevant equations

3. The attempt at a solution

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2. Feb 16, 2016

### HallsofIvy

Staff Emeritus
The formula you are using to find the integrating factor only applies to linear equations. This is not a linear equation!

3. Feb 19, 2016

### goldfish9776

that's why i multiply the whole equation with the integrating factor to get the exact equation , however , i didnt get it . Is my working totally wrong ? or which part is wrong ?

4. Feb 19, 2016

### Staff: Mentor

What integrating factor are you talking about? Your work up to the point where you say that the equation is not exact, but the work after that, I don't follow.

Since the DE is not exact, you might look for an integrating factor that is a function of x alone. If that doesn't work, you can see if there is an integrating factor of y alone. Finally, if that doesn't lead to an exact equation, you can try an integrating factor that is a function of both x and y.

5. Feb 19, 2016

### vela

Staff Emeritus
That's what the OP is trying to do. If the R(⋅) expressions had turned out to be functions of just x or just y, integrating them would yield the integrating factor. (Of course, it would have been nice if the OP had written the post properly and explained this instead of making us guess at what he/she was doing.)

6. Feb 19, 2016

### goldfish9776

do u mean R(x , y) , how to do it ? i have never studied this before

7. Feb 19, 2016

### vela

Staff Emeritus
8. Feb 19, 2016

### goldfish9776

9. Feb 19, 2016

### vela

Staff Emeritus
Not really. All I'd be doing is repeating what's on that page, which is pretty clear. Maybe someone else can chime in.

10. Feb 19, 2016

### goldfish9776

can you be fore specific , telling me how should i start with ?

11. Feb 19, 2016

### Staff: Mentor

@goldfish9776, are you sure you have copied the problem correctly? I tried to make the equation exact by first multiplying by f(x), and then by g(y), with no luck. Did you look at the link that vela gave?

12. Feb 20, 2016

### SammyS

Staff Emeritus
@goldfish9776 ,

Have you copied the problem correctly?

Are you certain that you haven't interchanged M and N .