The order of the differential equation `((d^3y)/(dx^3))^2 + ((d^2y)/(dx^2))^2 + ((dy)/(dx))^5`=0 is

Options

A. 3
B. 4
C. 1
D. 5

Answer

To determine the order of the given differential equation

\[ \left(\frac{d^3y}{dx^3}\right)^2 + \left(\frac{d^2y}{dx^2}\right)^2 + \left(\frac{dy}{dx}\right)^5 = 0, \]

we need to identify the highest derivative present in the equation.

### Step-by-Step Solution:

1. **Identify the derivatives**:
- The first term is \(\left(\frac{d^3y}{dx^3}\right)^2\), which involves the third derivative of \(y\).
- The second term is \(\left(\frac{d^2y}{dx^2}\right)^2\), which involves the second derivative of \(y\).
- The third term is \(\left(\frac{dy}{dx}\right)^5\), which involves the first derivative of \(y\).

2. **Determine the order of each term**:
- The order of the first term (third derivative) is 3.
- The order of the second term (second derivative) is 2.
- The order of the third term (first derivative) is 1.

3. **Find the highest order**:
- The highest order of the derivatives present in the equation is 3 (from the first term).

4. **Conclusion**:
- Therefore, the order of the differential equation is **3**.

### Final Answer:
The order of the differential equation is **3**.

---