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Proof of an integral using substituion methods

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Can you explain how you get from: dx derivative of (x^2 +9), divided by square root of (x^2+9) to: 3 sec^2 divided by 3 sec? I was given it as part of an answer to the ode: square root of x^2+9 dy/dx = y^2. Thank you.

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Proof that y = -1/Sqrt{x^2/9 +1} +x/3 +const from the differential equation y^2 = Sqrt{x^2 + 9}*dy/dx using substituion methods letting x = 3*Tan(theta)

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