Integrating factor Puns

Alright, so I'm practising first order differential equations, but I keep getting stuck on this one problem:

x*y' - 3y = x^3; y(1) = 10

y' - 3/x * y = x^2

Next you need the integrating factor:

P(x) = 3/x

rho(x) = exp(integral 3/x dx)

Now when I calculate this I get:

exp(3ln(x)) = exp(ln(x^3)) = x^3

But Symbolab gives 1/(x^3) and I don't understand why?

After this I just need to solve:

d/dx(y*rho(x)) = rho(x) * Q(x)

Hello,

Is it possible to find an integrating factor which is dependent on both x and y? Can you please suggest an analytical or numerical method that can be used for this purpose?

Hi everyone,

We create a simple video for the derivation of the integrating factor of linear equations. We tried to presented it using manim latex futures. How does it seem? Clear or not? Thanks in advance ıntegrating factor

I've seen so many formulas for solving integrating factors

First Type:

https://www.youtube.com/watch?v=v5C0CtRAK10

Second Type:

https://www.youtube.com/watch?v=is-Q0FuYGqk

Third Type:

https://www.youtube.com/watch?v=YJBQN7rYktk

I really don't know a universal way of turning an inexact D.E. into an exact D.E. out of these three ways of solving for the integrating factors. There are equations that work for the first type but doesn't work on the second and third. There are also equations that work for the third type and doesn't work for the latter.

Example:

Let's say we are given the D.E.: dy/dx = x-2xy

The given equation works for the first type but doesn't work on the second and third no matter how much I transform it into the respective forms of the second and third types.

Here's another example:

(y-xy)dx + xdy =0

The given equation works for the second type but doesn't work on the first and third regardless of any transformation techniques.

I am really confused and I do not know which types or techniques to use in terms of solving inexact differential equations. The third one is what I don't get the most as it is very confusing and there are too many forms to memorize. Please help me understand this topic. This is my only problem in first-order differential equations.

Hi guys, how do I solve this differential equation without an integrating factor?
The solution mentions to make use of the product rule, giving:
xy'+y=(xy)', then
(xy)'=2x
but I dont understand this part. Thanks!

When finding integrating factor, how do i know if the factor is a function of x, y or xy.

For example for the question below

4xdx+((4x^2)y+3y)dy=0

I assumed integrating factor is a function of x but i didnt get answer. When i assumed it is a function of y, I got it right. So what is the basis ?

Greetings, I am trying to resolve tree diff equations for a submittable homework. Though iI have reviewed the procedures over and over the system keeps telling me that my answer is wrongs... So I'll leave here the differential equations and the results so you guys can share some light on me, please... I am aware of the Reddit code of behavior though so anything you guys prompt me to do, I'll respect it.

Question 1

The solution of (1+x^2)y′+2xy=2x with initial value y(0)=0

In this question i calculate the integrating factor as 1+x^2 and the function y(x) = x^2/2

Question 2

The solution of x2y′=1−2xy with initial value y(1)=2

Integrating factor is'x' and the function y(x)=x+1/x

Question 3

The solution of y′+λy=a with initial value y(0)=0y and λ>0

here i've calculated the integrating factor as e^λx and the function is y(x)=a(1-exp(-λx))

I'm very confused because after doing them over and over again the answaer are still wrong, so i am trying to rule out that the problem is in the grading system.

Cheers

https://www.youtube.com/watch?v=onIh8xT97II

In this video we go through the step by step process of deriving a formula for the general solution of linear first order differential equation and the integrating factor in a way that's comprehensive and very easy to understand

https://www.youtube.com/watch?v=RxBsTaWZbHA&feature=share

Here is a follow up video to the previous one in which The formula for the General Solution and the integrating factor was derived. In this video the same process is used to solve actually Linear First order Differential Equations. This is added to the Differential Equations Playlist. Next upload will be on Separable Equations.

I’m sitting in front of the differential equation: (cosx)dx+(1+2/y)sinxdy=0 , and I need to solve it by finding an appropriate integrating factor, however, the equation does not appear to be linear, exact, or homogeneous, and so I’m at a loss for where to start. Does anyone have any insights?

I'm interested in partitioning a plant genome by function using ChIP-Seq data and a tool like ChromHMM, but I'm not familiar with the potential pitfalls of combining multiples types of ChIP-Seq data for this purpose. There is public ChIP-Seq data based on over 100 transcription factors and also on histone modifications like H3K4me3. I'm thinking that although there may be some overlap between transcription factor binding sites and histone marks, combining them should give the greatest information on functional genomic regions. Most studies tend to use only the histone modification data for partitioning. Is there a reason not to combine the two? Or does it make sense to integrate these ChIP-Seq data?

Having some trouble understanding this example of the integrating factor in Diff Eq. I'm assuming to get y by itself, they divide by the e^(-3x). There's an e^(-3x) on the other side of the equation, so why don't they cancel? The answer is y=-2+ce^(3x). How is it not just y=-2+c?

Link to my work: https://imgur.com/a/BfBpa1I

I uploaded a screenshot of the problem here. So basically I am to use the method of integrating factors to solve the general solution to y' + 13t^(12)y=t^13

The problem informs me that I should use the variable I in place of the integral of e^(t^13), to simplify the process. However once I attempt to integrate the RHS after multiplying it by my integrating factor m(t) = e^(t^13) the answer I get is always zero.

My online homework says that zero is not an acceptable answer for this problem, and I cannot figure out what I am doing wrong. Any and all help is vastly appreciated, thank you!

edit: formatting

Hi everyone, I know most of you must be happy that the final exams were cancelled but this leaves us with the burden of submitting high-quality IAs. Speaking of IAs, I'm doing my Maths HL IA currently on the SIR model and I wanted to make it HL-worthy by solving the differential equations in the model. I have considered other options such as the Euler method but I want to use the integrating factor method to derive the model but I'm not even sure if the integrating factor method can be used for the SIR model. Can anyone share a source or link that would help me with this?

Hi, my name is kyle and I am taking an online diffi equ course. Im learning how to use integrating factor to solve linear first order differential equations. I am confused, can you only use integrating factor to solve ODE's when their is no coefficient in front of y'.

Example: (x^2 + 1)*y' + xy = 0 -------> could you solve this using integrating factor since (x^2 + 1) is in from of y' ? Do you have to move the (x^2 +1) around to be able to solve this?

I'm in a sophomore-level ODE class right now and someone asked if this was possible. My professor said he wasn't sure. Is there a way to use the method of finding and multiplying by an integrating factor twice, somehow?

So I'm having problems with this text.

I'm confused when they get to the part where they say "Since the left side contains only first degree..."

Why can they rewrite the equation like that? I don't understand the logic behind tagging on an x to p(x) and a y to q(y)

I feel like something simple is just going over my head rn

https://www.youtube.com/watch?v=RxBsTaWZbHA

In this video we we solve a couple of First Order Linear Differential Equations using the same process we explained in the previous video in which we derived a formula for such equations

https://www.youtube.com/watch?v=RxBsTaWZbHA&feature=share

Here is a follow up video to the previous one in which The formula for the General Solution and the integrating factor was derived. In this video the same process is used to solve actually Linear First order Differential Equations. This is added to the Differential Equations Playlist. Next upload will be on Separable Equations.

https://www.youtube.com/watch?v=RxBsTaWZbHA&feature=share

Here is a follow up video to the previous one in which The formula for the General Solution and the integrating factor was derived. In this video the same process is used to solve actually Linear First order Differential Equations. This is added to the Differential Equations Playlist. Next upload will be on Separable Equations.

https://www.youtube.com/watch?v=RxBsTaWZbHA&feature=share

Here is a follow up video to the previous one in which The formula for the General Solution and the integrating factor was derived. In this video the same process is used to solve actually Linear First order Differential Equations. This is added to the Differential Equations Playlist. Next upload will be on Separable Equations.