Checking my separable differential equation solution

[hpayandah]

Homework Statement

Can someone please verify if I am solving this equation right.

Homework Equations

Please refer to attachment.

The Attempt at a Solution

Please refer to attachment.

 

[lanedance]

how about checking by differentiating
$$sin(y) = \frac{A}{\sqrt{x^2+1}}$$

$$\frac{d}{dx}sin(y) = \frac{d}{dx}\frac{A}{\sqrt{x^2+1}}$$

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

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

$$cos(y)dy(x^2+1)= -sin(y)2x.dx$$

which is looking ok, you probably want to use your initial condition though