https://file.aiquickdraw.com/mathbot/file/1728951013835eihyl2ro.jpg

I'll extract and analyze the mathematical equations from your uploaded image, then solve the equations step by step.

Here are the extracted equations:

1. \( \tan(y) \, dx - \cot(x) \, dy = 0 \)
2. \( (12x + 5y - 9) \, dx + (5x + 2y - 3) \, dy = 0 \)
3. \( x \frac{dy}{dx} = y + \sqrt{x^2 + y^2} \)
4. \( x \frac{dy}{dx} + y + x^3 = 0 \)
5. \( y \, dx - x \, dy = x^2 y \, dy \)
6. \( \frac{dx}{dt} + 3x = e^{2

Solve question 1 to 18 from the image provided by the user.

This set of problems includes solving 18 differential equations involving concepts like implicit differentiation, separable equations, trigonometric identities, and exponential functions. Step-by-step solutions guide the process, suitable for undergraduate students studying calculus or differential equations.

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