Linear equation and linear differential equations

I remember noting from an algebra class that x and y of a linear equation neither divide or multiply with each other which is somewhat clear from the forms of linear equations:

General form of linear equation:

$Ax+By+C=0$

Slope intercept form:

$y=mx+b$

Is this also true for linear differential equations?

The definition goes like this: "A differential equation is said to be linear if the dependent variable and its differential coeficients (derivates) occur only in the first degree and not multiplied together."

$\frac{dy}{dx}=Py+Q$

Where P, Q are functions of x only. What exactly does this mean?

Does the algebraic linear equation has something to do with linear differential equation?

I remember noting from an algebra class that x and y of a linear equation neither divide or multiply with each other which is somewhat clear from the forms of linear equations:

General form of linear equation:

$Ax+By+C=0$

Slope intercept form:

$y=mx+b$

Is this also true for linear differential equations?

The definition goes like this: "A differential equation is said to be linear if the dependent variable and its differential coeficients (derivates) occur only in the first degree and not multiplied together."

$\frac{dy}{dx}=Py+Q$

Where P, Q are functions of x only. What exactly does this mean?

Does the algebraic linear equation has something to do with linear differential equation?