5

(3y + 10c) (y F 3c)y =0 y(0)...

Question

(3y + 10c) (y F 3c)y =0 y(0)

(3y + 10c) (y F 3c)y =0 y(0)



Answers

Solve the differential equation.

$ 3y'' + 4y' - 3y = 0 $

In this problem, we have to solve the differential equation. Why Double prime minus six y prime plus nine y is equal to zero so forthis kind of differential equation. We can always associative characteristic a creation, which is going to be D squared minus six times D plus nine years ago to zero. Now this implies D minus three. Whole squared is equal to zero thirties. They called to three. In this case, we see that we have only one solution. So the fundamental solution it's going to be easy to the power three x and x Times E to depart three extra. Remember anybody on the same route? Then the fundamental solutions becomes X times E to the poor that route time. Six. So then that general solution it's going to be some constant c. One times e to depart three Ex Placido times X times It'll be poor three X

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 want to solve the differential equation. Three white double crime is he called to four white crane, which can be leading us three white, double brain minus four white prime mystical to zero. So now we can associate a characteristic equation. So this is going to be three D Square. Minus 40 is a call to zero. So this in place tee times three T minus four is equal to zero. So the same place either t is equal to zero Ortiz a call to four over three. So now we have the two routes off the characteristic in creation. So we see that don't start are real and distinct in this case, that Gino solution is going to look like C one Dave's e todo por ti Time six. So zero times six plus C, two times e to the power. So let's go back. So four over three four over three X now eternal Placido. We already know that's the call to one. So this is going to be C one plus C two times e to the power for X over three. So their star 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.


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