The degree of the differential equation `(d^3y)/(dx^3)+x((dy)/(dx))^4 = 4 log ((d^4y)/(dx^4))` is

Options

A. 1
B. 3
C. 4
D. Not defined

Answer

To determine the degree of the given differential equation

\[ \frac{d^3y}{dx^3} + x\left(\frac{dy}{dx}\right)^4 = 4 \log\left(\frac{d^4y}{dx^4}\right), \]

we need to follow these steps:

### Step 1: Identify the highest order derivative
The highest order derivative in the equation is \(\frac{d^4y}{dx^4}\).

### Step 2: Check the presence of transcendental functions
The equation contains the term \(4 \log\left(\frac{d^4y}{dx^4}\right)\). The presence of the logarithm (a transcendental function) applied to the highest order derivative indicates that the degree of the differential equation cannot be defined.

### Step 3: Conclusion about the degree
Since the degree of a differential equation is defined only when the highest order derivative appears in polynomial form (i.e., not inside a transcendental function), we conclude that the degree of this differential equation is **not defined**.

### Final Answer
The degree of the differential equation is **not defined**.

---