So the problem is
y''(t) + q(t) y(t) = 0
Where q(t) = -i*(omega - omega_0) e^{2*i*omega*t}. I'm not quite sure how to solve this, I can already imagine it's really simple but it's missing me at the moment. Any help is appreciated!
hi i am new to control. would anyone be able to explain how to solve simultaneous non linear differential equations in order to find steady state conditions. i dont know where to start. thanks!
I'm working on 2nd order linear ODEs learning about general solutions for that but the book doesn't mention anything about non-linear solutions.
I'm guessing no, but how do people go about solving these DEs? Is this where numerical methods come into play?
Hello, I'm currently trying to fill the gaps in my knowledge by self-learning mathematical concepts from differential equations, probability and statistics, to linear algebra. I'm studying them to prepare myself for eventual computational biology applications (like in enzyme kinetics). I'd like to know if you have tips and how to learn these subjects and what would be the best sources available for people coming from a mainly biology background.
I usually learn through doing many exercises and practice problems, starting from the simple and banal ones to more complex ones. Doing many exercises and practice problems and then comparing my solutions to the answers given by the resources themselves usually help me interiorize concepts. For example, doing the very basic exercises and practice problems from the Chemistry Workbook for Dummies actually helped me in my university chemistry studies. I want to know if there are equivalent workbooks designed for slow but eager learners like me in linear algebra, statistics, etc. that I can use for my self-study sections. I believe there is also a "Differential Equations Workbook for Dummies" but I have yet to check it out since I'm currently focusing on my linear algebra foundations.
Only if I'm stuck with a problem that I then actively look for a relevant Youtube videos (first choice) and then textbooks (second choice) in order to clarify concepts. I actually tend to prioritize Youtube videos before passing on to textbook explanations since the latter tends to be too abstract to me. I prefer the visualizations provided by Youtube videos, in which step-by-step problem-solving processes are usually shown.
I don't know if there are interactive materials/courses that I can access for free, but I'd love to try them too. If you have workbook or website (or Youtube channel) suggestions, please let me know.
5y''+3y'+2|y|=f(t)
It's just the absolute values that is throwing me off, but I believe it's linear.
I'm going off of this.
https://preview.redd.it/tfngyu8w3ki11.png?width=638&format=png&auto=webp&s=562ec0513f27c7eb4f6c5bd84df56279033ef965
So I took single variable calculus I and II in junior year of high school. This semester in college I am taking linear algebra/differential equations, what topics are important for me to review and what should I start studying. Also, I haven't taken multivariable calculus yet. Please let me know, I'm worried. Thank you.
How to solve an equation like:
d²x/dt² + w² x = -a x^5
Given the initial conditions: x(0) = x0 dx(0)/dt = 0
I can't seem to grasp this concept.
Edit: After reading the responses and searching google, I finally get it now! Thanks guys! :))
Hey guys! I just completed my linear algebra and differential equations classes and man, both of those were pretty difficult but thankfully, it's over. Although that got me wondering if it's really over, like would I need to use these concepts again in future classes? I didn't find much on my school's CS curriculum page but I think I remember hearing that linear algebra is heavily used in machine learning? Anyways, just curious if you guys know whether these kinds of complex math classes (complex for me) are used in any specific classes or electives at the upper level. Perhaps I'll have to do some preparation if I intend on choosing those upper level classes
I got the following assignement:
> The following system is to be analyzed: dx/dt=y^3 − 4x, dy/dt=y^3 −y−3x. > > (a) Find all the fixed points and classify them. > > (b) Show that the line x=y is invariant, meaning that any trajectory > starting on this line stays on it subsequently. > > (c) Show that |x(t)−y(t)|→0 as t→∞. > > (d) Plot an accurate phase portrait, on a square domain −20≤x,y≤20.
I managed to to point a,b and d but do not know how to tackle point c.
I imagine I have to solve the differential euqations each and just show that the absolute value of both of them is the same for t = infinity.
But how do I get the solutions to x(t) and y(t)?
I'm looking for the intuition behind it, not a formal proof.
Here's the question.
What I've so far thought of is the fact that as the function goes to infinity dy/dx has to equal 0, and it further proves this because sin(2Pi) = 0 (when you plug y=9/2) and based on that, what I tried doing was factoring the first part of the DE, getting roots 4,5 but I don't really understand what I can do with that.
Furthermore, I'm not sure exactly how I can use the initial condition to solve the question.
Any help is appreciated!
I'm not sure if this makes sense - but I'm wondering what the eigenvalues of something like
x' = (x - k)(x^2 + k^2 -1)
Or are they just for when there's a system?
In a non linear system of differential equations, to classify the points of equilibrium as unstable or stable why do we need to compute the jacobian matrix of that system on those points (and then find the eigenvalues)?
So I took single variable calculus I and II in junior year of high school. This semester in college I am taking linear algebra/differential equations, what topics are important for me to review and what should I start studying. Also, I haven't taken multivariable calculus yet. Please let me know, I'm worried. Thank you.
