Is there a bug in this math program?

**s3a** · March 21st 2010, 02:42 PM

Is there a bug or am I simply making a mistake in the following example?:

Question:
Find a function

of

such that

?

My Answer:
sqrt(1/5 * x^2 - 1)

I ask because the program does not say that it's wrong but it doesn't say that it's right either. In fact, it says "Can't generate enough valid points for comparison." So, IF I am right, I am going to email my teacher to inform him so if anyone could confirm, it would be greatly appreciated!

Thanks in advance!

**Miss** · March 21st 2010, 02:46 PM

Let us see your work.
This is a separable equation.

**s3a** · March 21st 2010, 02:59 PM

What exactly does "separable equation" mean? Like I know it is separable, I just don't know why. I only know it is separable because that's all I think we're doing in my course (at least for now). And, my work is attached.

**Archie Meade** · March 21st 2010, 03:03 PM

Originally Posted by s3a

Is there a bug or am I simply making a mistake in the following example?:

Question:
Find a function

of

such that

?

My Answer:
sqrt(1/5 * x^2 - 1)

I ask because the program does not say that it's wrong but it doesn't say that it's right either. In fact, it says "Can't generate enough valid points for comparison." So, IF I am right, I am going to email my teacher to inform him so if anyone could confirm, it would be greatly appreciated!

Thanks in advance!

$5y\frac{dy}{dx}=x$

$\frac{d}{dx}\left(\frac{5y^2}{2}+C\right)=\frac{dy }{dx}\frac{d}{dy}\frac{5y^2}{2}=5y\frac{dy}{dx}$

$\frac{d}{dx}\left(\frac{x^2}{2}+C\right)=x$

Your work looks good to me!

**s3a** · March 21st 2010, 03:29 PM

Okay thanks, I contacted my teacher to tell him that it's a bug. But could you help me with the theory...what does "separable" mean? As for "differential equation," I'm guessing it just means something about equations and their derivatives or something like that.

**Archie Meade** · March 21st 2010, 03:50 PM

Originally Posted by s3a

Okay thanks, I contacted my teacher to tell him that it's a bug. But could you help me with the theory...what does "separable" mean? As for "differential equation," I'm guessing it just means something about equations and their derivatives or something like that.

a seperable differential equation can be written as

$N(y)\frac{dy}{dx}=M(x)$

and this is the equation you have.

Then $N(y)dy=M(x)dx$

Once the variables x and y are seperated, you can integrate both sides.
You can think of a differential equation as one that contains a derivative.

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