4

Clult U cente masd 4tk nlt R-{lxy) Ocycxst} 4 nat "nu-nnit-me Plx_ =X...

Question

Clult U cente masd 4tk nlt R-{lxy) Ocycxst} 4 nat "nu-nnit-me Plx_ =X

Clult U cente masd 4tk nlt R-{lxy) Ocycxst} 4 nat "nu-nnit-me Plx_ =X



Answers

$2 y^{2}-3 y-2$
12. $2 w^{2}+5 w-3$
13. $3 n^{2}+13 n+4$

Hello and welcome to this video solution of numerous. Here we are given a link comprehension. So here in statement one were given that and iron or a on roasting with sodium carbonate and lying in the presence of air gives to compound PNC. And you're from option the second part the solution be in concentrated. It's alan reaction with production furrows and it gives a blue color on precipitated of compound their cost solution of C. On treatment with considerate statistical gives a yellow colored compound E. And the compound even treat it with a seal gives an orange red compound F. Which is used as an ox raise anything. So you have to make certain predictions to come into the solution. So let me show you how it's made. So first of all we take for if he oh she had to poetry thus eight and a two freedom global neck And with air that is given seven or 2 good line gives you to a free two or three that's eight the name so Seattle four. That's it. It's a frustration. Next we have if we two or three reacting with concentrate sales that is given gives you who official three Last three H 2. Right now this official tree reacts with who before if he 10 6 that is protection fellow sign a great this gives you the blue solution pushing blue solution of if the four if he CN six whole trade plus 12 cases. Mm Next From three we have two any he wanted to see our well for That's 8/10 of food gives you we need to the odd 47 is the yellow color solution. Greatness in A. Two so four. That's it too. No you have in A to see our two or seven. Okay, last case here is the orange color substance of people pr two or seven that's 2010. So this is the so let us state what is A what is B. The first we have me is If you see a 23, this is a Next we have every two or 3 SCB or Yes. So this suits also be ready And in in 204 this is C. Right BNC. That is mentioned. Yes. Now this pushing blue books. Mhm. Yeah. Yeah. Whoa it is. Mhm. Okay. To see again this election with the this one your local er this is E and we have orange. What are some common? It does if Yeah. Right. I hope this is clear to you and have a very good rest of the day. Thank you.

This problem gives them virtual equation, which I'm writing on the board and then asked us to find in the form of this equations particular solution. So to do that, we'll have to look at the equation and use a method of undetermined coefficient. So we write the operator l of y described the left hand side as why Triple Prime plus three y double prime minus four y In terms of the differential operator B, this is D cubed plus three D squared minus for acting on why which we will come back to in a minute. So, based on the method of undetermined coefficients, are particular solution will be of the form X to the S than a M. A constant times X m added with decreasing values of the exponent of X to get at a one x plus A not times eats the Rx with these guys, depending on the information from our equation. So defined s wants to have to wait and second to we get our for him. We look at the X terms that we have, which we don't have any here, so our end is going to be equal to zero. So then the only term we have from this is a not And so for our are we look at the value of the exponents on the E negative to eggs. So are are is going to be equal to negative two to find s we see if our is a root of this equation this but this is equal to zero with are plugged in. So first we just plug this in for be negative two cubed plus three times negative two squared minus four. This is negative eight plus three times four minus four which is equal to negative 12 combining the negative eight negative four plus to us, which is equal to zero. So we actually know that are are is a route, but we don't know if it could possibly be a double or triple room. So for that, we're going to have to use the quadratic formula here. I'm starting a quadratic formula. We're goingto have to end up factoring this well when we ride it out like this D cubed plus B squared minus +460 weaken Duthie squared factor out of the plus through minus four people zero looking and negative two for d we already know would end up giving us zero, but we have it squared here. So then it would be a double root. X is equal to two because this to here. And so then a particulate solution would be of the form X squared because s equals two times just a Not because in is equal to zero and then eats the negative two x and this is would be a not X squared e to the negative, too. Then that is a form of our particular solution.

Okay, so here we want to find the solution for why Triple Prime Plus Three. Why double primaries for why is equal to G two in the motive to X. So we consider the corresponding homogeneous equation of R cubed plus three R squared minus four. Okay, into that, the only factor is equal to R minus one times are plus two squared. And so when we set that equal zero, um, this is going to have an are equal toe one and are equal to negative two with a multiplicity to. So that means our general solution to the homogeneous part Call that Y h It's gonna be equal to some constant times e to the power of native to X for some other constant times X times e to the power of negative two X and then possum third constant times each of the power of X. So this X, that's a front is here because of the, uh, multiplicity of to Okay, so now we want a particular solution and we will look for a particular solution of the form a X squared times E to the negative two x. Okay, So from there we get that are particular solution. First derivative is equal to to a x Times e to the negative two x minus two A x squared eat negative two x Excuse us a second derivative just equal to two a e to the negative two x minus eight A eggs e to the negative two x plus four A x squared e to the negative two x and why Triple prime I'm dropping the functional notation here, um, handing on how strict your professors are. Email it to include it, but our third rivet is equal to negative 12 a e to the negative two X plus 24 A x e Teoh Negative two X minus eight A x squared e to the negative two x This will take, uh, the equation we started with that. Why? Triple crime plus three wide double prime minus four. Why is equal to eat the native to X Ever gonna insert? Uh, thes particular solution functions and they deliver. Driven is into the great places in there. And so that's gonna give us negative 12 a. E to the negative two X plus 24 a X e to negative two x minus eight A x Squared E to the negative two x plus six a e to the negative two x minus 24 a X e to negative two x plus 12 a x squared e to the negative two x minus four e x squared e to the negative two x and that will be equal to actually lots and lots of cancellations. Here's this whole thing ends up simply being equal to negative six a e the negative two x right. And so that we set that we had this right hand side which I largely ignored here. So this is equal to e to the negative two x So we just want to compare those Constance s so that have a negative six A on the left hand side should be equal to one or rather, a should be equal to negative 1/6. Yes, we can plug that in for a particular solution which was of the form a X squared eating native to X is gonna be negative 16 X squared E to the negative two x We'll get our Why by adding are homogeneous solution toe a particular solution. So the full solution is going to be native. 16 x squared e to negative. Two x plus c. One e negative. Two x plus c. Two X e to the negative. Two x plus c three e to the power of X and that's it.


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