Polio drops are delivered to 50K children in a district. The rate at which polio drops are given is directly proportional to the number of children who have not been administered the drops. By the end of `2^("nd")` week half the children have been given the polio drops. How many will have been given the drops by the end of 3rd week can be estimated using the solution to the differential equation `(dy)/(dx)=k(50-y)where x denotes the number of weeks and y the number of children who have been given the drops.
State the order of the above given differential equation.

Answer

To solve the problem, we need to analyze the given differential equation and determine its order.

### Step-by-Step Solution:

1. **Identify the Differential Equation**:
The given differential equation is:
\[ \frac{dy}{dx} = k(50 - y) \]
where \( y \) is the number of children who have been given the drops, \( x \) is the number of weeks, and \( k \) is a constant of proportionality.

2. **Determine the Order of the Differential Equation**:
The order of a differential equation is defined as the highest derivative present in the equation. In this case, the highest derivative is \(\frac{dy}{dx}\), which is the first derivative of \(y\) with respect to \(x\).

3. **Conclusion**:
Since the highest derivative is the first derivative, we conclude that the order of the given differential equation is:
\[ \text{Order} = 1 \]

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

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