What is an example of a inseparable diff-eq

Question

anonymous · Answer

dy/dx = x + y

anonymous · Answer

Cant I just seperate that into -y dy = x dx?

anonymous · Answer

No, you can't.  The algebra doesn't work at all.

lukecrayonz · Answer

What math is this o.O

anonymous · Answer

If you try, you get:

dy = (x + y) dx

etc.

anonymous · Answer

A differential equation that can not be solved by separating the variables.

2y''+3y'+y=5

anonymous · Answer

@luke: this is introductory ordinary differential equations

lukecrayonz · Answer

I meant like, the name of the math class, as in like Calculus, Pre-calc, Trig etc.

anonymous · Answer

I don't understand why subtracting y in that case is an illegal move?

anonymous · Answer

An ODE y' = f(x,y) is separable if we can write f(x,y) = g(x)h(y) and hence

dy/h(y) = g(x) dx

With the equation

y' = x + y 

there is no such factorization of the right hand side into two functions exclusively in x and y.

anonymous · Answer

Given y' = x + y, then

dy = (x + y) dx

so yes in principle you can now write

dy - y dx = x dx

but that is not in separable form.

anonymous · Answer

Makes sense.

anonymous · Answer

Luke: I should let Meta say what this is for him specifically.  But in general terms this is either one of the very last topics in Calculus, the first topic in Differential Equations (a course that comes after Calculus), or perhaps Applied Mathematics, which uses a variety of tools.

anonymous · Answer

@luke Calculus 2.

lukecrayonz · Answer

D: Only 2 years away.