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Idealist10
Group Title
Find the general solution of (x2)(x1)y'(4x3)y=(x2)^3.
 one month ago
 one month ago
Idealist10 Group Title
Find the general solution of (x2)(x1)y'(4x3)y=(x2)^3.
 one month ago
 one month ago

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Idealist10 Group TitleBest ResponseYou've already chosen the best response.1
@myininaya
 one month ago

Idealist10 Group TitleBest ResponseYou've already chosen the best response.1
@beccaboo333
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
so i assumed you tried to put in the form y'+p*y=q form
 one month ago

Idealist10 Group TitleBest ResponseYou've already chosen the best response.1
Please help me. How do I start? Divide (x2)?
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
divide by (x2)(x1)
 one month ago

Idealist10 Group TitleBest ResponseYou've already chosen the best response.1
Okay, I'll try and tell me what's going on. Please don't leave.
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
you may have to some partial fractions just to let you know
 one month ago

Idealist10 Group TitleBest ResponseYou've already chosen the best response.1
But how do I integrate (4x3)/((x2)(x1))?
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
partial fractions
 one month ago

Idealist10 Group TitleBest ResponseYou've already chosen the best response.1
So do I multiply (x2)(x1)? It's x^23x+2.
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
\[\frac{34x}{(x2)(x1) }=\frac{A}{x2}+\frac{B}{x1}\] before you integrate you write what is on the left hand side in the right hand sides's form you must find A and B to complete that transaction
 one month ago

Idealist10 Group TitleBest ResponseYou've already chosen the best response.1
So 4x/(x2)3/(x1)? And 4x(x1)3(x2)? But equal to what?
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
... Have you ever done partial fractions before?
 one month ago

Idealist10 Group TitleBest ResponseYou've already chosen the best response.1
So isn't it 5ln(x2)ln(x1)?
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
I will show an example: \[\frac{1}{(x5)(x3)}\] pretend we wanted to write this as a sum of proper fractions we can attempt to do this by trying to write that fraction in this form A/(x5)+B/(x3) To find what A and B are we will need to combine those fractions in put in to form that is 1/[(x5)(x3)] form. so let's do that \[\frac{A}{x5}+\frac{B}{x3}=\frac{A(x3)+B(x5)}{(x5)(x3)}=\frac{(A+B)x3A5B}{(x5)(x3)}\] but the other side is equal to 1/[(x5)(x3)] so that means the other can have no x's so A+B would have to be 0 and the constant term will have to be equal to 1 therefore 3A5B=1 so we have a system of linear equations to solve: A+B=0 3A5B=1  To solve I will try to setup for elimination Multiply first equation by 3 3A+3B=0 3A5B=1 now add 2B=1 B=1/2 If B=1/2 and A+B=0, then A=1/2 So you know that \[\frac{1}{(x5)(x3)} \text{ can be written as } \frac{1}{2} \frac{1}{x5}\frac{1}{2}\frac{1}{x3}\] and we know how to intgrate both of those terms
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
@Idealist10 for the integrating factor there was a negative sign in front of y term so take what you have and multiply it by 1 but don't forget the integrate factor has that base e thing so for integrate factor we should have \[v=e^{5\lnx2+\lnx1}\] This can be a lot prettier
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Now that was just one example above from partial fractions There are other things to consider when writing a fraction composed of polynomials as a sum of fractions
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
What I'm saying is the section on partial fractions can not be explained by one example
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Anyways back to what you were saying...
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
to write your integrating factor a lot prettier you will need to recall some law of exponents and also some log properties
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
you do recall that x^(a+b) can be written as (x^a)(x^b) ?
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
do you see how that could be helpful here?
 one month ago

Idealist10 Group TitleBest ResponseYou've already chosen the best response.1
Yes, wait a second.
 one month ago

Idealist10 Group TitleBest ResponseYou've already chosen the best response.1
So I got v=(x1)/(x2)^5, is this right?
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Very good!
 one month ago

Idealist10 Group TitleBest ResponseYou've already chosen the best response.1
Let me work it out then.
 one month ago

Idealist10 Group TitleBest ResponseYou've already chosen the best response.1
Yes, I got it! Thank you so much! Wow, this is a tough problem to solve!
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
Probably mostly because of the partial fractions part?
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
I guess you are in differential equations and try to recall all the things you learned in calculus 2. I do agree I had some trouble but with practice it should become easier on what you should do when you see something like that.
 one month ago

myininaya Group TitleBest ResponseYou've already chosen the best response.1
just practice practice it will sink in eventually
 one month ago
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