Linear Differential Equations

[wooden basalt]

Are these Linear Differential Equation or a Non - Differential equation?

1. y = x'

2. y = x^2 + 2

I was watching a YouTube video on it and in the video the second equation was described as a non-Linear Differential Equation and I can't tell why

[fair ibex]

It’s a non linear differential equation

You can tell because of x^2 term

x is a function and basically.

x’=x^2+2

If it was linear, there wouldn’t be a x^2 term

[wooden basalt]

So does it mean x has to have a maximum power of 1?

[fair ibex]

Yeah

[wooden basalt]

For it to be a Linear one?

[fair ibex]

Yea

It’s like a linear function y=ax+b

[wooden basalt]

Oh ok
But what of the first one

[severe badger]

Degree 1 is linear

X^1

[wooden basalt]

Do you mean y is a function of x
As in y=x^2 + 2?

[fair ibex]

You got two differential equations there?

Or just 1

[wooden basalt]

2 different equations

They aren't related

[fair ibex]

If it’s separate then, they are not differential equations

We don’t have something like y’=ay^n+b

y=x’ you would mean y=y’ then?

[wooden basalt]

The first question was
y=x'

And the second question was
y=x^2 + 2

[fair ibex]

What is x’

[wooden basalt]

As in y = x prime

differential of x

[wooden basalt]

Differential of x

[fair ibex]

You mean y=dx/dy?

x’ is a function of y

Usually we write an differential equation with the same function y both sides

[wooden basalt]

Yes but I guess that is the same as y = x'

[fair ibex]

So you are trying to find x(y)?

[wooden basalt]

I'm confused

[fair ibex]

Me too

[wooden basalt]

No

I'm just asking why y = x ' is a Linear D. E

[fair ibex]

There’s a problem with that differential equation

Let me send you something

[wooden basalt]

Oh sorry I guess the person meant x raised to the first power instead of x prime because he concludes that x raised to 1 is a Linear Differential equation

[wooden basalt]

OK sure

I think it's because the one was so short

[fair ibex]

An example of a differential equation

Where is x’ coming from

You are supposed to have derivative of y = something in terms of y

y=y’ would be a differential equation

But y=x’ no since x’ is not y’

Who sent you these equations?

[wooden basalt]

YouTube skancity academy

[fair ibex]

What’s the title of the video

[wooden basalt]

Title is 03 Linear and non differential equations

[fair ibex]

Okay thanks

I’ll check right now

Okay

[fair ibex]

These are equations not differential equations

[wooden basalt]

Oh ok

[fair ibex]

He put an example of what is a linear equation and what is a non linear equation

He didn’t talk about differential equations yet

Non linear equation is for example y=3x^2+2

[wooden basalt]

Oh ok so the first one is a Linear equation and the second one is a non Linear one

[fair ibex]

Yes

This is absolutely not a differential equation

[wooden basalt]

But they are not DEs

[fair ibex]

Yea

Not DEs

[wooden basalt]

Oh ok thank you very much for your help

[fair ibex]

Youre welcome!

[wooden basalt]

Do I have to close it now?

I mean the channel

[fair ibex]

In case you need help in some actual differential equation I could be there

[fair ibex]

If you want

[wooden basalt]

Oh ok thanks

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