- #1
maistral
- 240
- 17
L[y2] = ?
maistral said:L[y2] = ?
maistral said:I'm slowly starting to get it.
I read this article in wikipedia: http://en.wikipedia.org/wiki/Riccati_equation
are the q0, q1, and q2 constants or functions of x? because the S = q2q0 looks like a constant multiplication of sorts. Or i have to multiply the functions?
also, v' = v^2 + R(x)v + S(x) -> what is this lol
I so hate wikipedia notations =.=
maistral said:Argh, my net broke.
Anyway, I still need a little help. I need to build it myself :( To ease myself of all those qn(x)'s, I use this notation:
y' = A + By + Cy2
where A, B, and C are functions of x.
So to solve this analytically, I do a change of variables. I let y = -(1/C)*(u'/u). What would be my y'?
is y' = -1/C * [(u*u" - (u')2)/u2] + [u'/u * -c'/c2]?
Is there an easier way for this? surely this looks ugly, but there might be other ways that I'm not aware of.. Also, whatever happened to the (u')2? Ofc unless my answer is wrong, and someone has to review differentiation e.e
Sorry for the barrage of questions. I'm such a noob
F(s) = 4/s
G(s) = sinh4t
thus;
f(t-v) = 4
g(v) = 1/4 cosh4t
-int(0,t,4*cosh4t dt) = 4/4 cosh 4t = -cosh4t
The Laplace Transform of L[y2] is a mathematical operation that transforms a function of time, y(t), into a function of complex frequency, Y(s). It is denoted as L[y2] = Y(s) and is used to solve differential equations and analyze the behavior of dynamic systems.
The Laplace Transform of L[y2] is calculated using the following formula:
L[y2] = ∫ e-sty(t)dt, where s is a complex frequency and t is time. This integral can be evaluated using tables or with the help of software such as MATLAB or Wolfram Alpha.
The Laplace Transform of L[y2] has several properties that make it a useful tool in solving differential equations. These properties include linearity, time-shifting, differentiation, integration, convolution, and initial value theorem. These properties can be used to simplify the calculation of Laplace Transforms and solve complex problems.
The Laplace Transform of L[y2] has various applications in engineering, physics, and other fields. It is used to analyze the stability of control systems, solve circuit problems, and model physical systems. It is also used in signal processing, image processing, and data analysis.
The Laplace Transform of L[y2] is a powerful tool, but it does have some limitations. It can only be applied to functions that have a Laplace Transform, and it may not work for all types of differential equations. Additionally, the inverse Laplace Transform may not always exist, making it difficult to get the original function back.