Question

The rate of change of y with respect to x is proportional to the difference between y and 5. (a) Write a differential equation for the statement. (Use k for the constant of proportionality.) dy dx

Answer 1

Answer:

$\frac{dy}{dx}=k(x-5)$

Step-by-step explanation:

The rate of change of $y$ with respect to $x$ is proportional to the difference between $y$ and $5$.

Rate of change of $y$ with respect to $x$ is equal to $\frac{dy}{dx}$

Difference between $y$ and $5$ is equal to $y-5$

The rate of change of $y$ with respect to $x$ is proportional to the difference between $y$ and $5$.

So,

$\frac{dy}{dx}$ ∝ $y-5$

Take $k$ as a constant of proportionality.

$\frac{dy}{dx}=k(x-5)$