1. Explicit form

On this differential equation I was asked to find a particular solution with y= 4 and x= 0. Which I did, now I have to find the explicit form of that particular solution.

Here is the question and my answer:

Find the explicit form of this particular solution.
y-1/2 = (2+sin x)-1 + 3/8

The explicit solution is obtained by making y the subject of the equation

y= (2 + sin x)^1/2 +3/8

I multiplied -1/2 both side

2. Originally Posted by valerie-petit
I multiplied -1/2 both side
No, you didn't.

1) I can't tell what it is you have written. Is that $y^{-1/2}$ or $y - \frac{1}{2}$ or something else?

2) If you intended the former, multiplication would not do the job.

3) If you intended the latter, multiplication would not do the job.

4) If you intended either, how did the "3/8" manage to sit there, so taciturn in its position?

5) This sort of error must raise questions why you are dabbling in differential equations. Please review some elementary algebra. It will save you if it is solid.

3. Re:Explicit

I don't know how you became a SuperMember.

So much for the help, no! you prefer pick on people who try to learn.

And by the way I wanted to say: do I have to multiply(forgot question mark)

I'm really dissapoint of people like you who think they know everything. I just starting to learn the integration, I'm not ' a SuperMember' like you.

And for Rekoner say what you have to say instead of applause other people badness.

4. It is amazing how often honesty is mistaken for personal affront. I'm not making any value judgments. You don't need to do it either.

Rather than being upset, did you try answering my questions? Notice 1) and 4) in particular. Simply answer the questions and we can learn something.

If you had included the original problem statement, it is likely I could have figured out what you meant. Alas, you did not provide that information.

More information is almost always better than less information. In this case, the inclusion of the ORIGINAL problem statement would have gone a long way. You did show your results, but very little of your work.

Let's assume x and y are positive.

Rules of exponents
$y^{1/2} = x+4 \implies y = (x+4)^2$

$y - 1/2 = x + 4 \implies y = x + 9/2$

I'm just not seeing any multiplication in there.

Multiplication
$y(1/2) = x + 4 \implies y = 2x + 8$

I ask again, what is it that you mean? Just answer the question.

5. Re:Explicit

1) I try to write : y^-1/2 = (2+sin x)^-1 + 3/8

4) 3/8 it is replacing c the arbitrary constant.( you see in a previous exercise I was ask to find the corresponding particular solution (in implicit form) that sastifies the initial condition y= 4 when x= 0. Which I did that's why you see 3/8)

And now I'm ask to find the explicit form of this particular solution.

Actually I'm working on it but I'm sure with lot of mistake:

y^-1/2 = (2+sin x)^-1 + 3/8

½ = y

Hence the explicit form of the particular solution is

y= ½(2+sin x)^-1 + 3/8

6. Okay, I see we are having a little language barrier problem.

y^-1/2 normally would mean $y^{-1/2}$ and one cannot remove the -1/2 by multiplication. It's an exponent and requires exponential operations.

If you mean this: $y^{-1/2}\;=\;(2+\sin(x))^{-1} + \frac{3}{8}$

Which is the same as this: $\frac{1}{y^{1/2}}\;=\;\frac{1}{2+\sin(x)} + \frac{3}{8}$

Then you will have to do a little work to pretty it up for a solution. I suggest this:

$\frac{1}{y^{1/2}}\;=\;\frac{8+3(2+\sin(x))}{8(2+\sin(x))}$

Simplfying the Numerator
$\frac{1}{y^{1/2}}\;=\;\frac{14+3\sin(x)}{8(2+\sin(x))}$

Reciprocal Properties
$y^{1/2}\;=\;\frac{8(2+\sin(x))}{14+3\sin(x)}$

Finally, the Exponent
$y\;=\;\left(\frac{8(2+\sin(x))}{14+3\sin(x)}\right )^{2}$

This is why I suggested that you may wish to review some algebra. There was NO calculus in there just now. It was all algebraic manipulation that must be done correctly or, frankly, the calculus is of no value.

Note: It will also be to your benefit to learn a little LaTeX. Inline mathematics is sometimes quite ambiguous and difficult to translate. Properly formatted text makes communication much simpler.

7. TKHunny

I apologize for my previous message I thought you were being smart.

Thanks again TKHunny, for your help, I'm going to take a closer look at laTeX