Question

x=logp and y=1/p differential equation

Answer 1

To find the differential equation involving the variables x and y, we can express y in terms of x and then differentiate it. Let's proceed with the given equations:

x = log(p) (Equation 1) y = 1/p (Equation 2)

First, let's solve Equation 1 for p: x = log(p) p = e^x (where e is the base of the natural logarithm) Now, substitute the value of p in terms of x into Equation 2: y = 1/p y = 1/(e^x)

To find the differential equation, we differentiate Equation 2 with respect to x:

dy/dx = d/dx (1/(e^x)) Using the chain rule: dy/dx = -1/(e^x) * d/dx(x)

Since d/dx(x) is equal to 1, we have: dy/dx = -1/(e^x)

So, the differential equation involving the variables x and y is: dy/dx = -1/(e^x)