1. ## Few questions about the nature of differential equations

Hello,

if I have an ODE without the initial conditions (e.g f(2) = 1), can I solve it with Laplace transform?

Are differential equations with constant coeffcients linear? Or are they equal to LTI system? (Linear time invariant)

Thank you.

2. ## Re: Few questions about the nature of differential equations

Yes, you can use the Laplace transform. Just leave the initial values as undetermined constants.

No, being "linear" and having "constant coefficients" are completely different things. $y''- 2(y')^2+ cos(y)= e^x$ has "constant coefficients" but is not "linear" while $e^x y''- cos(x)y'+ x^3y= ln(x)$ is "linear" but does not have "constant coefficients".

3. ## Re: Few questions about the nature of differential equations

Oh, ok. So LTI is differential equations with constant coefficients?

4. ## Re: Few questions about the nature of differential equations

Sorry, I meant LTI systems are differential equations with constant coefficients and DE must be linear?

5. ## Re: Few questions about the nature of differential equations

What is "LTI" short for?

6. ## Re: Few questions about the nature of differential equations

Well, it's short for Linear Time Invariant. It's linear, and time invariant means that it doesn't change, (coefficients).

7. ## Re: Few questions about the nature of differential equations

Originally Posted by Nforce
Well, it's short for Linear Time Invariant. It's linear, and time invariant means that it doesn't change, (coefficients).
Is my statement correct?

I have another question, are Time invariant systems also static, so to speak? Are then dynamic systems time variant, where coefficients do not change?

Thanks.

8. ## Re: Few questions about the nature of differential equations

Sorry, but can someone answer my question? Or no one knows what am I talking about?