What is the order of `(y'')^(2)+cos y'=0` ?

Answer

To determine the order of the differential equation \((y'')^2 + \cos(y') = 0\), we need to analyze the highest derivative present in the equation.

### Step-by-step Solution:

1. **Identify the derivatives**:
- In the given equation, \(y''\) represents the second derivative of \(y\) with respect to \(x\).
- The term \(y'\) represents the first derivative of \(y\) with respect to \(x\).

2. **Examine the highest derivative**:
- The highest derivative in the equation is \(y''\), which is the second derivative.
- The term \((y'')^2\) indicates that we are squaring the second derivative, but it does not change the order of the derivative itself.

3. **Determine the order**:
- The order of a differential equation is defined as the highest order of derivative present in the equation.
- Since the highest derivative here is \(y''\), which is a second derivative, the order of the differential equation is 2.

### Conclusion:
The order of the differential equation \((y'')^2 + \cos(y') = 0\) is **2**.