# Thread:

1. ## Solve for y...

I'm doing differential equations and got stuck on this part.

How do I solve for y if I have the equation:

-siny = x^2 + C

Thanks

2. Originally Posted by jzellt
I'm doing differential equations and got stuck on this part.

How do I solve for y if I have the equation:

-siny = x^2 + C

Thanks
$-\sin y = x^2 + C$

$\sin y = C-x^2$

$y = \sin^{-1}(C-x^2)$

3. Originally Posted by pickslides

$y = \sin^{-1}(C-x^2)$
Shouldn't it be minus c as well?

Here's what I got:

$-\sin y = x^2 + C$

$\sin y = -C-x^2$

$y = \sin^{-1}(-C-x^2)$

OR

$y = -\sin^{-1}(C+x^2)$

4. Originally Posted by Educated
Shouldn't it be minus c as well?
Its a constant $\displaystyle c\in \mathbb{R}$ , why should it be negative?

5. Maybe this is why I'm still in high school.

Just ignore me then... I haven't learnt those things yet.

EDIT:

Wait...

$\displaystyle c\in \mathbb{R}$

c is and element of a real number...

Isn't -c a real number? Why isn't -c allowed?

6. Originally Posted by Educated

c is and element of a real number...
Therefore can be positive or negative.

7. Since C is an arbitrary real number, it doesn't matter whether C is positive or negative and it doesn't matter whether we call it "C" or "- C". The same thing happens often with exponentials. If you have a solution to an equation of the form $e^{x+ C}$ where C is an arbitrary constant, you can write that as $e^{x+ C}= e^C e^x$ or simply as $C e^x$. Strictly speaking, we should use a different symbol, say C' with the explanation that $C'= e^C$ but typically, knowing that they are both just arbitrary numbers, that is not done.
{"extraction_info": {"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": 14, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.9494322538375854, "perplexity_flag": "middle"}