Why Does dy Change in Solving Linear Differential Equations?

[robertjford80]

Homework Statement

I don't understand why in step 2 dy turns into d and why +P(x) dissappears
I also don't see a difference between v(x)y and v(x)*y

In step three why does the d disappear. I see that dx is going over to the right side, well, what about the numerator d?

 

[clamtrox]

d/dx is the differential operator. dy/dx just means d/dx operating on y. You should probably read a bit more elementary calculus to get used to this notation.

You start from a differential equation
$$\frac{dy}{dx} + P(x) y = Q(x)$$
and then you multiply both sides of this equation with a function $v(x)$ (which you have to find first) which has the property that the left hand sides of steps 1 and 2 are equal.

In step 3, you integrate both sides of the equation with respect to x.