Need help making sure I'm doing a substitution correctly

[EGill]

I have attached a word document that shows all the work and equations.

Your help is appreciated.

 

[JThompson]

$$x\left[\frac{dv(x)}{dx}+1\right]=\left[v(x)\right]^{3}+v(x)+x$$

$$\mbox{ is correct, but the equation after it}$$

$$f \left[\frac{1}{v(x)^{3}}+\frac{1}{v(x)}\right]dv=\frac{1}{x}dx$$

$$\mbox{does not follow- you incorrectly manipulated the first equation.}$$

$$\mbox{Try multiplying the x through in the } x\left[\frac{dv(x)}{dx}+1\right]\mbox{ term, and then try to separate the variables.}$$

 

[EGill]

Thanks for the response. Took forever, but I have managed to do it correctly further along now.

I am still stuck at another point. The new attachment shows all my work again

 

[Mark44]

You have an error.
I'm assuming that your work is correct up to where you said you're confident.

ln(u - x) - (1/2)ln[(u - x)² + 1] = ln(x) + C

<==> ln(u - x) - ln[(u - x)² + 1]^1/2 = ln(x) + C

Now combine the two log terms on the left side using the property that ln(a) - ln(b) = ln(a/b).

Also, on the right side you have e^{ln(x) + C} becoming Cx. The first C is different from the second C. They're both constants, but they are different ones, so you should use a different letter or mark the second one to note that they are different.

 

[EGill]

$$ln\left[\frac{u-x}{((u-x)^2+1)^{1/2}}\right]=e^{ln\left[x\right]+c$$

$$\frac{u-x}{((u-x)^2+1)^{1/2}}=Dx$$

Would this be correct? Since C is a dummy variable i figured I could reuse it, but I see your point.

Also, this was my first time trying to type a formula into the reply. Whenever I hit preview post it would refresh, but the post would not reflect the changes in the equation area. I had to reload the page to get the post to reflect the changes in equation. Am I doing something wrong. Just trying to learn how to do it without word docs if it is just one equation.

 

[JThompson]

That is correct. And no, you aren't doing something wrong inputting Latex code.. for some reason you have to refresh the page to view changes using preview post.

 

[Mark44]

Also, this was my first time trying to type a formula into the reply. Whenever I hit preview post it would refresh, but the post would not reflect the changes in the equation area. I had to reload the page to get the post to reflect the changes in equation. Am I doing something wrong. Just trying to learn how to do it without word docs if it is just one equation.

As I understand things, the LaTeX script is cached on your computer, so when you start a post and click Preview Post, the previous LaTeX script, if any, is displayed, not the script you just entered. This is a known problem. The workaround is to refresh the web page. That will display the right LaTeX script.