# Linear equation and linear differential equations. General form of linear equation: Ax+By+C=0. Slope intercept form: y=mx+b. Is this also true for linear differential equations?

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?
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acorazarxf
Step 1
It's saying that if x and y (or their derivatives) are multiplied together in any way, it's not considered a linear differential equation because it's not solvable in the usual ways that linear ODE's are.
Step 2
This relates to normal linear equations in that if you have an equation where x and y are multiplied or otherwise modify each other in a way that prevents strict separation in the polynomial, they do not have a linear relationship. For example, the plot of $y=1/x$ is not a line while $y=x$ is.