Eliminating Arbitrary Constants: Solving the Differential Equation

[manal950]

Homework Statement

From the differential equation by eliminating the arbitrary constant from the equation
(y - b ) ^2 = 4 (X-a )

http://www7.0zz0.com/2013/02/02/21/747681463.png

 

[mfb]

What do you want to do?
The first equation is not a differential equation, and can be solved for y (or x) easily (not with the steps shown in the image).

 

[epenguin]

Probably means form the differential equation.

Well, just differentiate through by x.

 

[manal950]

(y- b ) ^2 = 4 (X- a )

2(y-b)dy/dx = 4 (divide by 2 )

(y-b)dy/dx= 2

then what should I do

 

[Dick]

(y- b ) ^2 = 4 (X- a )

2(y-b)dy/dx = 4 (divide by 2 )

(y-b)dy/dx= 2

then what should I do

I don't know what you are trying to do. Yes, (y-b)dy/dx=2. So dy/dx=2/(y-b). If that's what you want to do you are done. You now have a differential equation for y without the initial condition constant.

 

[manal950]

yes now

dy/dx=2/(y-b)

but after that what must I do ?

( 2/dy/dx )^2 = 4(X-a )

 

[mfb]

Post the full problem statement please.
We have no idea what you want/have to do, as it is your homework and not ours.

 

[epenguin]

You have formed a differential equation by eliminating an arbitrary constant. That seems to be what you were asked but as Dick says, we have had to guess a bit.