5

8 Solve using Green's function_y" _ 4y = &2ry(0) = 0, y(0) = 0....

Question

8 Solve using Green's function_y" _ 4y = &2ry(0) = 0, y(0) = 0.

8 Solve using Green's function_ y" _ 4y = &2r y(0) = 0, y(0) = 0.



Answers

Solve the differential equation.

$ y'' - 4y' + 13y = 0 $

Okay, And you're eights. Why will find that minus 14? Why Prime was 15. Why's it to John? Did you write this as 18? I'm just great when it's Fortune Lambda was Christine is equal to zero. It's all for Orlando's Using our quadratic equations will get negative closet where Jimmy plus minus square root before she and scored minus four a. C all over. Two times eight. Which is a This gives me for two plus minus. Curve it four times 71 eye over 16 and the simplifies to seven over its plus minus crew of 70 71 I over eights. So let's let this cool Alfa was beat up. So since our solutions are there, we have conflicts congregate with Our solution is in every. Why is it could be to our Alfa, which is seven over 86 times C one co sign of our beta, which is square roots. Perhaps anyone over eight X. I must see to Ryan uh, the one who screwed us everyone over eight Sex

Hello Friends. We have to solve that given defense electrician's a weekend. I did do you to buy upon D. X square plus develop on the X months of it very close to zero. This is the second order homogeneous equation. So we can also write it like this. This car vipers divide monastery very close to zero. So actually a question will be like this. I was really a question about this baby. Mm square bless em month 80 calls to zero. Okay, so the rules of the seclusion will be A man and M two. So that is a cost to and one is -1 Plus Square Root of 33.2. Mt will be management manners of schools of 33 upon to. Okay, this is the rules of the other equation. So we can write the solution vehicles to seven and then seven into even to the power of and annex policy too. You do the power of M two x. Okay, so we can decide via calls to seven into into the power of management minus one plus the square root of 33 upon two of X. Plus you two into into the power minus one minus of this court of 33 upon two of x. Mhm. Mhm. So why will be costume U to the power of -X. Y. two is common seven into it. To the Pavlov Square root of 33 to upon X. Placido into two departments of the square root of 33 upon two of X. So this is the answer. So mm I hope you understood.

In this problem, we have to solve the differential equation. Four y double crime plus four white prime. Plus Why is it called a zero forthis kind of differential equation? We can always a specific characteristic aggression when she looks like four times T squared, plus four times T plus one is called a zero. Now this implies this is according to 30 plus one. Whole square is equal to zero, so the simplest easy call to negative half. So he's a call to negative half. It's the double jute off dark actress stick excavation. So whenever we have the same wrote that occurs in the characteristic decoration, so then the fundamental solution is going to be e to the power. Negative half X comma extends Edo the bar negative half X So then the general solution is going to be wise to goto some constant c one times e to the power negative X over too plus C two times x you to rip our negative X over too. So that's the general solution forthis differential equation

The given equation we redid amounts diva learned last. All right equals You drive to the par -3. Now this is a Bernoulli equation you know, standard from has given us these are by the last B in Taiwan. You and do what? And we're being years old. Excellent beeping forex and kill me. It really is minus not to solve this. I mean Solution. We used to wipe our 1- and which is all right. We have a baby. I want to be in Yeah. Or like you do you like the multiply creation one right? Or like you do you remember? Yes. You mean like the hopes for what? Yeah, says devi my dear last I mean mhm. Yes. Mhm. Right now this is a linear equation. We know that the linearity has the standard from the rebranding. Yes. Even into we need you won The P one is 16 XQ one is 32 works both being functions the long all this before indeed in fact over. Mhm. DeParle the one being come with us immigration. Do you know the year? Yes. Yeah. Uh huh. Multiplied into the integrating exactly this. E mm correct. DVs and then Right. Yeah. Need to be a texas square into the right Okay people it's all right. This is nothing but the by the exhaust V into E power A texas right little X. And keep our IT. Now let's integrate both sides. We get we into you follow right equal stew integration two you brother. This is where let's assume be as he takes as well. We get DT my dear. Uh huh. Dina this integration victims the world the power the the comes us to keep our steve Yeah. You two x squared of me. Yes. Why powerful equals two two. No, he he power minus no.


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