first order de

Question

The degree of the differential equation (dy/dx)³ + 2(dy/dx)² + y = 0 is

RankGuru · Accepted Answer

1. **Definition of Degree**: Once a differential equation is expressed as a polynomial in its derivatives, the degree is the power of the highest order derivative.
2. **Identify Highest Order Derivative**: The highest derivative here is $\frac{dy}{dx}$ (order 1).
3. **Identify Power of that Derivative**: The term $(\frac{dy}{dx})^3$ contains the highest derivative raised to power **3**.
4. **Check Validity**: The equation is a polynomial in derivatives, so the degree is well-defined.

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