https://file.aiquickdraw.com/mathbot/file/1726055324854p4mfqjab.jpg

The image shows two equations with arbitrary constants. To eliminate the arbitrary constants from these equations, we can differentiate them or use other techniques as appropriate. Let's look at both:

1. **Equation 9:**
   \[
   y = (C_1 + C_2x + C_3x^2) e^{2x}
   \]
   Here, \( C_1 \), \( C_2 \), and \( C_3 \) are arbitrary constants, and we need to eliminate them.

2. **Equation 10:**
   \[
   y = (C_1 + C_2x) \sin x + (C_3 + C_4x) \cos x
   \]
   Again, \( C_1 \), \( C_2 \), \( C_3 \), and \( C_4 \) are arbitrary constants.

To eliminate the arbitrary constants, we typically differentiate these equations repeatedly until the constants disappear. Would you like me to proceed with differentiating these equations and explaining how to remove the constants step by step?

Explore the step-by-step process of eliminating arbitrary constants from equations like y = (C1 + C2x + C3x^2)e^(2x) and y = (C1 + C2x)sin(x) + (C3 + C4x)cos(x). This guide involves differentiation techniques commonly used in advanced calculus.

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