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Solve y" 4y 4y = 0 f You ac told that at keast onc of the solutions periodic with period...

Question

Solve y" 4y 4y = 0 f You ac told that at keast onc of the solutions periodic with period

Solve y" 4y 4y = 0 f You ac told that at keast onc of the solutions periodic with period



Answers

Solve the differential equation.

$ 4y'' + 4y' + y = 0 $

In this problem, we have to solve the differential equation. Why? Double prank minus four. White crane plus 13. Why is it called to zero? Now we can associate the characteristic equation, which is going to be D square minus fourth Dynasty plus 13 is equal to zero. Now let's try to solve this quadratic equation. So T is going to be negative. Be so negative. Off negative four plus minus Squire rode off B square, so negative force Squire minus for a seat four times one times 30 divided. Fight two times a day. So two times one. So this is going to be four plus minus square root off 16 minus 52 divided by two which is going to be four plus minus. Squire rode off Negative 36 divided by two. So finally I will end up getting too plus minus three heart iota What I owed a negative one. So now we see that the roots Salter characteristic equivalent are complex numbers in this case. So let's recall that you're in. So if our one is it called too Alfa. Plus I'm Peter and are too. Is he called to Alfa minus Iveta Art, though routes off the characteristic excavation characteristic equation. So then we know the solutions are going to be you to the poor Al flicks Time See one times call sign Beata X plus C two Time Sign off B takes seeing our kids. We see that our Alfa is a call to to and our beater Is it going to treat? So then in our kiss, the general solution is going to be, he told the power. Two weeks time. See one time school sign off three X plus C two, then sign off three x So that's going to be oh, general solution for the differential equation.

In this problem, we have to solve the differential equation. Nine. Why? Double prime plus four times. Why is it called a zero? We can always associated characteristic equation Tau this kind of differential equation. So in this case is going to be nine t square plus four is equal to zero. So this implies T square is equal to negative fall off our nine so t is equal to plus minus to over three times. So now we see that the roots of the characteristic equation are complex number. So let's recall the Purim related to complex roots. So it says, if are the one. Is it called to Alfa? Plus I better and our two is it called to Alfa minus. I better art the dudes off the characteristic inauguration. Then the solution that general solution looks like C one times co sign off, Be tykes rusty to time, Stein off Beatrix. And then you have to multiply everything by sea to the power ALF likes. So that's how the general solution looks like. So now in our kiss, we see that Alfa is equal to zero and beat icicle toe to over three. So then that's another solution is going to be. Why is he calling Tau? See one for some constant course. Sign two weeks over three plus C two time sign off twigs over three.

In this problem, we have to solve the differential equation. Three white double prints plus four white crane minus three y is equal to zero. So let's write down that characteristic equation, so that characteristic equation it's going to be three t Square plus four times D minus three is equal to zero. So this implies TUC Call to negative be so negative. Four plus minus square root off the square, which is 16 minus four a. C. So four times three times negative. Three divided by two times a So it is three in this case, so I have negative for plus minus square root off. 16 now four times three strove 12 times three is 36. So I have 30 fix devices. Six. So which can be simplified? Us. Negative, too, by this quiet route or plus minus, squared it up. 13 Divided by treats. Now that the truth on dhe, the distinct Phil, that's general solution off district Menschel equation. It's going to be fee one time e to the power negative, too. Then let's take the positives. Time supports it. Starting divided by three 96 plus e to times E to the power make it if too negative. Squire Dude off 30 divided by three time six. So that's going to be but general solution off our differential equation.

He was both de function F Thanks e s periodic with the period. Could you say something? Could you stay here and now Unless I ever found the X zero Just done. The f X zero equals ju zero, and then we can find a own so ocean Judy equation F X in coaches. Oh, uh, expressed in terms on the set. X on, then thanks. They're a plus. The empty weather and here will be, uh, into true here.


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