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A) Find the general solution: y ^(7) + 2y^ (5) +y(^3)=0(b) Determine a suitable form for a particular solution Y (t) ifthe method of undetermined coefficients is to...

Question

A) Find the general solution: y ^(7) + 2y^ (5) +y(^3)=0(b) Determine a suitable form for a particular solution Y (t) ifthe method of undetermined coefficients is to be usedy^(7)+2y^(5)+y^(3)=4t^2+cost+2te^tNote: Don't evaluate the constant coefficient in Y(t) in partb

a) Find the general solution: y ^(7) + 2y^ (5) + y(^3)=0 (b) Determine a suitable form for a particular solution Y (t) if the method of undetermined coefficients is to be used y^(7)+2y^(5)+y^(3)=4t^2+cost+2te^t Note: Don't evaluate the constant coefficient in Y(t) in part b



Answers

For each of the differential equations,Find the values of $b$ that make the general solution: (a) overdamped, (b) underdamped, (c) critically damped. $$s^{\prime \prime}+b s^{\prime}+5 s=0$$

Hello. Today we're going to solve our problem Number 27 from section of you here. We had to find solution all the different elocution by using method of Yiddish off perimeters given because you have my number minor full. Why? Because five u to the power X. So when you find the general solution, that is by double Eskander, Liberty Square. My enough full. It goes so difficult. April's fool B equals Russell minus two. So dinner for the variety affects because Seaver, you know about off the books, plus single it about off minus two x here. Why you want? Because you feel about off works rightto because it is about off minus two x for you. The blue can be found out by W because you know about off the licks. This difference initiation. You prove it this to collect eres tu minus two x minus. Do it over off minus two weeks. So it comes to the line enough. Think so? Similarly, we can find young girls in the buying a slimer. My enough sort of minus light. Bush comfortable minus two legs in two f offense. Half off exes. Fiery Bella politics by, You know about all thinks they were by W W is full minus full for a trick on meth. Find by four In general, it apart off Minor thinks for it will be gone. Minus five by full. You know about my ethics. Soon it'll be in bed. Why run out for fixed by W Why one is you do about the works and for offenses fire you toe the products developed by the blues minus four. So it becomes minus five by four in the girl it about off three x It becomes my last five by the way. Into the bar 30 x So if I want to be right toe Yeah, I would be right to gamble it on us minus five by four. You know the boat off my an ethics into a beautiful but off lex minus five by Well, it is about off three X indeed. A lot off minus two. It if these are very good. My enough. Fired by three that it is particle a pea by pea off. Ex con trick laceration minus 5.3 year fixed. Therefore, torture solution is it's where plus disliked So just a plus minus five by three. And don't you so well a solution? What given differential equation, But you think matter off. Thank you

All right. So let's go ahead and start off this problem by replacing these wipe terms with our terms instead. So Y double prime translates to R squared and why prime translates to our In the sequel C0. And now we have to do a little bit of factoring. So all we're gonna do is we're going to take out A. R. And we'll have our times are plus five which equals zero. And this gives us our values of zero and 9: five. So with these are values we can go ahead and build our solution. So our solution is going to be C one E 20 X Plus C. to eat the -5 x. We can go ahead and simplify this out since each of the zero access simply each of the zero which is one. So have y equals to see one plus C. Two. He's a -5 x. And that's your answer.

Okay, so we need to find the general solution to this. That means we need to find the corresponding auxiliary creation that's gonna be p of our is able to. And then we just place all the d with are So we have our plus one times ar minus five is equal to zero. So this is already factored. So our solutions are just gonna be negative one and positive five. So our general solution, it's just going to be Why of X is equal to C one e to the negative x plus C two e two the five X, like so.

Hollowed one today we're going to sort problem Number 25 from the section Tractor view here. The given differential equation is why people s Mina six light over there plus 25 via dies. He because x squared. So this can be again determined if all they killed minus six the square plus trendy fire D in court dozing off us, we will find the general solution. Do you coma? The square minus 60 plus to identify It goes so you look good. The Pecos zero comma three plus on wireless For so the general Sir, vision is Lyddie off x will be see when he restaurants around that issue are Think through it as 23 X god Forex bless scene three He rested three x Same for X is the general solution then particle A solution can be found out by here it is in to score. So by be off X because ever x plus and to every square Why do you guys x Because ever plus crew in tow Eggs Why do you number nice off x Because go and well it s a substitute in this because we got fear Oh my enough! I think Injured toe toe plus 25 injured even plus true a tow eggs because X squared combating coefficients speaking well, my last you are here too. Plus 25 everyone it could sell. Then 50 year toe equals zero A good Iran because a good, little foolish And if just a gentle solution this even plus you to your list three X growth forex plus scene three arrested, three x Sign for that's there. No far question. Thank you.


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