Integrating Factor Homework: Correctness & Complexity

[goldfish9776]

Homework Statement

is my integral R(x) and R(y) correct ? why it look so complicated ?

Homework Equations

The Attempt at a Solution

 

[HallsofIvy]

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

 

[goldfish9776]

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

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 ?

 

[Mark44]

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 ?

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.

 

[vela]

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.

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.)

 

[goldfish9776]

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.

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

 

[vela]

You might want to take a look at http://mathworld.wolfram.com/ExactFirst-OrderOrdinaryDifferentialEquation.html to get ideas. I don't think any of the specific cases they looked at works for this particular problem.

 

[goldfish9776]

You might want to take a look at http://mathworld.wolfram.com/ExactFirst-OrderOrdinaryDifferentialEquation.html to get ideas. I don't think any of the specific cases they looked at works for this particular problem.

i still didnt get the idea, can you explain further?

 

[vela]

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

 

[goldfish9776]

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

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

 

[Mark44]

@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?

 

[SammyS]

@goldfish9776 ,

Have you copied the problem correctly?

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