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.
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.
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. $\displaystyle y''- 2(y')^2+ cos(y)= e^x$ has "constant coefficients" but is not "linear" while $\displaystyle e^x y''- cos(x)y'+ x^3y= ln(x)$ is "linear" but does not have "constant coefficients".