Find the order of the following differential equations:
`(d^(2)y)/(dx^(2)) = sin x`

Answer

To find the order of the given differential equation \(\frac{d^2y}{dx^2} = \sin x\), we will follow these steps:

### Step 1: Identify the highest order derivative
The given differential equation is \(\frac{d^2y}{dx^2} = \sin x\). Here, we need to identify the highest order derivative present in the equation.

### Step 2: Determine the order of the derivative
The term \(\frac{d^2y}{dx^2}\) represents the second derivative of \(y\) with respect to \(x\). The order of this derivative is 2, as it is the second derivative.

### Step 3: Conclusion
Since the highest order derivative present in the differential equation is the second derivative, the order of the given differential equation is 2.

Thus, the order of the differential equation \(\frac{d^2y}{dx^2} = \sin x\) is **2**.

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