Degree of differential equation `(d^(2)y)/(dx^(2))+((dy)/(dx))^(3)+y=0` is :

Options

A. 3
B. 2
C. 1
D. 0

Answer

To find the degree of the given differential equation

\[ \frac{d^2y}{dx^2} + \left(\frac{dy}{dx}\right)^3 + y = 0, \]

we will follow these steps:

### Step 1: Identify the highest order derivative
The highest order derivative in the equation is \(\frac{d^2y}{dx^2}\).

### Step 2: Determine the order of the differential equation
The order of the differential equation is determined by the highest derivative present. Here, since \(\frac{d^2y}{dx^2}\) is the highest derivative, the order of the differential equation is 2.

### Step 3: Identify the degree of the differential equation
The degree of a differential equation is defined as the power of the highest order derivative when the equation is a polynomial in derivatives. In our case, the highest derivative \(\frac{d^2y}{dx^2}\) appears to the power of 1 (since it is not raised to any power).

### Step 4: Conclusion
Thus, the degree of the differential equation is 1.

### Final Answer:
The degree of the differential equation is 1.

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