Need help with this differential equation using separation of variables.

lilmul123
Messages
39
Reaction score
0

Homework Statement



The differential equation I have is dy/dx = (xy + 2y - x - 2)/(xy - 3y + x - 3). I need help getting started. Neither the top nor the bottom can be factored, so I don't know what to do next. Can anyone give me a push? All I know is that I need to use separation of variables.
 
Physics news on Phys.org
lilmul123 said:
Neither the top nor the bottom can be factored, so I don't know what to do next. Can anyone give me a push? All I know is that I need to use separation of variables.
The top and bottom can both be factored ... try again.
 
lilmul123 said:

Homework Statement



The differential equation I have is dy/dx = (xy + 2y - x - 2)/(xy - 3y + x - 3). I need help getting started. Neither the top nor the bottom can be factored, so I don't know what to do next. Can anyone give me a push? All I know is that I need to use separation of variables.

Hint: Your numerator can be factored:

(xy + 2y - x - 2) = y(x + 2) - (x + 2) = (x + 2)(y - 1).

Similarly in the denominator.
 
Oh, of course. Okay, so now I have (x+2)(y-1) on top, and (x-3)(y+1). I have separated those out. Now I have (y+1)/(y-1) dy = (x+2)/(x-3) dx. Is this the correct equation I need to solve?
 
Looking good so far :smile:
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

Differential Equation with an Initial condition
Replies
3
Views
3K
Finding the rate of change of x in the equation
Replies
8
Views
1K
Question on Two Differentiation Techniques
Replies
25
Views
2K
Using separation of variables in solving partial differential equations
Replies
1
Views
2K
Solving a Differential Equation by Separation of Variables
Replies
5
Views
1K
PDE and the separation of variables
Replies
11
Views
1K
Differentiate an equation to find the minimum peak of a variable
Replies
17
Views
2K
Using chain rule when one of the variables is constant
Replies
8
Views
1K
What is a Different Method for Implicit Differentiation?
Replies
2
Views
2K
Arbitrary constant in denominator
Replies
15
Views
2K

Hot Threads

Recent Insights

Back
Top