Homework Help: CALCULUS

Posted by Anonymous on Saturday, May 26, 2012 at 3:07pm.

Using the separation of variables technique, solve the following differential equation with initial condition:
(4x sqrt)(1 - t^2)(dx/dt) - 1 = 0 and x(0)=-2
I believe that the answer is one of the following two options:
a.) 2x^2 = arcsint + 8
b.) arccost + 8 - (1/2)pi

CALCULUS - Damon, Saturday, May 26, 2012 at 3:41pm
4 x dx = dt/sqrt (1-t^2)
2 x^2 = sin^-1 (t) + c
when t = 0, x = 2
8 = 0 + c
c = 8
so 2 x2 = sin^-1 (t) + 8
or
2 x^2 = cos^-1(t) + c
8 = pi/2 + c
yes, agree
CALCULUS - Anonymous, Saturday, May 26, 2012 at 5:42pm
I'm only permitted to choose one option. And seeing as you came up with arcsin first, would this be a better answer over the option with arccos?
CALCULUS - Damon, Saturday, May 26, 2012 at 6:51pm
They are the same.
cos (pi/2 - x) = sin x

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