Separable Differential Equation

1. Jan 24, 2012

hpayandah

1. The problem statement, all variables and given/known data
Can someone please verify if I am solving this equation right.

2. Relevant equations

3. The attempt at a solution

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2. Jan 24, 2012

lanedance

$$sin(y) = \frac{A}{\sqrt{x^2+1}}$$
$$\frac{d}{dx}sin(y) = \frac{d}{dx}\frac{A}{\sqrt{x^2+1}}$$
$$cos(y)\frac{dy}{dx} = 2A(x^2+1)^{-3/2}\frac{-1}{2}2x$$
$$cos(y) dy \frac{A}{\sqrt{x^2+1}} = -A(x^2+1)^{-3/2}2x.dx.sin(y)$$
$$cos(y)dy(x^2+1)= -sin(y)2x.dx$$