Answer:
We can place everything with v(x) on one side of the equality, everything with x on the other side. This is done on the step-by-step explanation, and shows that the new equation is separable.
Step-by-step explanation:
We have the following differential equation:
We are going to apply the following substitution:
The derivative of y is the derivative of a product of two functions, so
Replacing in the differential equation, we have
Simplifying by x:
Here, we have to apply the following ln property:
So
Simplifying by x,we have:
Now, we can apply the above ln property in the other way:
But
So:
We can place everything that has v on one side of the equality, everything that has x on the other side, so:
This means that the equation is separable.