Separable Differential Equation Question

  • #1

Homework Statement


dy/dx = (y^2 - 1)/ (x^2 - 1) with initial condition y(2) = 2

Why is y = 1 and/or y= -1 not solutions?


Homework Equations





The Attempt at a Solution



I am actually able to solve this differential equation but when I separate the equation according to x and y:

(y^2 - 1)^-1 dy = (x^2 - 1)^-1 dx

here I am dividing both sides of the equation by (y^2 - 1), which means now I have to exclude y = 1 , -1 and check whether they are solutions

Now how do I show that y =1 and y = -1 are not solutions?
 

Answers and Replies

  • #2
Dick
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Homework Statement


dy/dx = (y^2 - 1)/ (x^2 - 1) with initial condition y(2) = 2

Why is y = 1 and/or y= -1 not solutions?


Homework Equations





The Attempt at a Solution



I am actually able to solve this differential equation but when I separate the equation according to x and y:

(y^2 - 1)^-1 dy = (x^2 - 1)^-1 dx

here I am dividing both sides of the equation by (y^2 - 1), which means now I have to exclude y = 1 , -1 and check whether they are solutions

Now how do I show that y =1 and y = -1 are not solutions?

y=1 or y=(-1) don't satisfy y(2)=2, do they? They are solutions to the differential equation but they don't satisfy your boundary condition.
 

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