# Diff. Eq. change of variable

• Dec 2nd 2008, 10:29 AM
diablo2121
Diff. Eq. change of variable
$y ' = x + y$

$u = x + y$

We're supposed to solve the eq. using u, but we have not covered change of variables in class, and I'm having troubles with partial derivatives.

$\frac{du}{dx} = dx + y$

$\frac{du}{dy} = x + dy$

Differentiating in terms of x and y leave those, but I don't know what to do with those. We're trying to find $\frac{dy}{dx}$, but I can't seem to find that in terms of u and x.
• Dec 2nd 2008, 10:41 AM
running-gag
Quote:

Originally Posted by diablo2121
$y ' = x + y$

$u = x + y$

We're supposed to solve the eq. using u, but we have not covered change of variables in class, and I'm having troubles with partial derivatives.

$\frac{du}{dx} = dx + y$

$\frac{du}{dy} = x + dy$

Differentiating in terms of x and y leave those, but I don't know what to do with those. We're trying to find $\frac{dy}{dx}$, but I can't seem to find that in terms of u and x.

Hi

I suppose u and y are functions of x
$\frac{du}{dx} = 1 + \frac{dy}{dx}$ and $\frac{dy}{dx} = x + y$

So $\frac{du}{dx} = 1 + u$
This is a 1st order differential equation
{"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 13, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "url": "http://mathhelpforum.com/differential-equations/62893-diff-eq-change-variable-print.html", "fetch_time": 1502986653000000000, "content_mime_type": "text/html", "warc_filename": "crawl-data/CC-MAIN-2017-34/segments/1502886103579.21/warc/CC-MAIN-20170817151157-20170817171157-00053.warc.gz", "warc_record_offset": 266147745, "warc_record_length": 2881, "token_count": 373, "char_count": 1157, "score": 3.953125, "int_score": 4, "crawl": "CC-MAIN-2017-34", "snapshot_type": "longest", "language": "en", "language_score": 0.9558353424072266, "file_path": "/sailhome/yjruan/project/latent-lm/data/processed/finemath-4plus/finemath-4plus/train-00044-of-00064.parquet"}