# Solve for y...

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• Sep 13th 2010, 07:29 PM
jzellt
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
• Sep 13th 2010, 07:34 PM
pickslides
Quote:

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

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

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

$\displaystyle y = \sin^{-1}(C-x^2)$
• Sep 13th 2010, 09:51 PM
Educated
Quote:

Originally Posted by pickslides

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

Shouldn't it be minus c as well?

Here's what I got:

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

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

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

OR

$\displaystyle y = -\sin^{-1}(C+x^2)$
• Sep 13th 2010, 09:57 PM
pickslides
Quote:

Originally Posted by Educated
Shouldn't it be minus c as well?

Its a constant $\displaystyle \displaystyle c\in \mathbb{R}$ , why should it be negative?
• Sep 13th 2010, 10:00 PM
Educated
Maybe this is why I'm still in high school.

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

EDIT:

Wait...

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

c is and element of a real number...

Isn't -c a real number? Why isn't -c allowed?
• Sep 13th 2010, 10:16 PM
pickslides
Quote:

Originally Posted by Educated

c is and element of a real number...

Therefore can be positive or negative.
• Sep 14th 2010, 03:34 AM
HallsofIvy
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 $\displaystyle e^{x+ C}$ where C is an arbitrary constant, you can write that as $\displaystyle e^{x+ C}= e^C e^x$ or simply as $\displaystyle C e^x$. Strictly speaking, we should use a different symbol, say C' with the explanation that $\displaystyle C'= e^C$ but typically, knowing that they are both just arbitrary numbers, that is not done.