A Veterinary doctor was examining a sick cat brought by a pet lover. When it was brought to the hospital, it was already dead. The pet lover wanted to find its time of death. He took the temperature of the cat at 11.30 pm which was `94.6^(@)F`. He took the temperature again after one hour, the temperature was lower than the first observation. It was `93.4^(@)F`. The room in which the cat was put is always at `70^(@)F`. The normal temperature of the cat is taken as `98.6^(@)F` when it was alive. The doctor estimated the time of death using Newton law of cooling which is governed by the differential equation: `(dT)/(dt) prop (T − 70),` where `70^(@)F` is the room temperature and T is the temperature of the object at time t.
Substituting the two different observations of T and t made, in the solution of the differential equation `(dT)/(dt)`=k(T-70) where k is a constant of proportion, time of death is calculated.
State the degree of the above given differential equation.

Answer

To solve the problem and determine the degree of the given differential equation, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Differential Equation**:
The differential equation given is:
\[ \frac{dT}{dt} = k(T - 70) \]
where \( T \) is the temperature of the object (the cat) at time \( t \) and \( k \) is a constant of proportionality.

2. **Determine the Highest Derivative**:
In the equation, the highest derivative present is \( \frac{dT}{dt} \).

3. **Identify the Power of the Highest Derivative**:
The power of the highest derivative \( \frac{dT}{dt} \) is 1, since it is not raised to any power other than 1.

4. **State the Degree of the Differential Equation**:
The degree of a differential equation is defined as the power of the highest derivative. Since the highest derivative \( \frac{dT}{dt} \) has a power of 1, we can conclude that:
\[ \text{Degree of the differential equation} = 1 \]

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

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