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For each example below, find the values of the parameters (constants) and so that the function y(t) satisfies the differential equation. If there is more than one c...

Question

For each example below, find the values of the parameters (constants) and so that the function y(t) satisfies the differential equation. If there is more than one correct value separate them bY commas (e.9. 3,2). You may enclose them in curlies if you prefer (e.9. {3,2} ). ( y' meansy(t)=ett satisfies y' - 12y = 0 ifr =y(t)=e(tIs) satisfies Y' - 4 t19y = 0 ifr=andy(t)=t" satisfiesE y = 0 if r =y(t)=cos (t satisfiesy" + 12 y = 0 if @

For each example below, find the values of the parameters (constants) and so that the function y(t) satisfies the differential equation. If there is more than one correct value separate them bY commas (e.9. 3,2). You may enclose them in curlies if you prefer (e.9. {3,2} ). ( y' means y(t)=ett satisfies y' - 12y = 0 ifr = y(t)=e(tIs) satisfies Y' - 4 t19y = 0 ifr= and y(t)=t" satisfies E y = 0 if r = y(t)=cos (t satisfies y" + 12 y = 0 if @



Answers

find the particular solutions of the given differential equations that satisfy the given conditions. $D^{4} y+3 D^{3} y+2 D^{2} y=0 ; \quad y=0$ and $D y=4$ and $D^{2} y=-8$ and $D^{3} y=16$ when $x=0$

Hello. We have to find a political solution that is Due to five minutes divi mhm consume 12 by By constant European Mexico zero And very close to one When exposed to one. So we can add the housing education mm square minus M Ministry because 20 M -4 into M -M Plus three. The cost zero assembled v. And one will be four and empty will be modest. three So solution will be buy costumes so listen can bitterness vehicle to seven U. to the Power four x. Yes you do into the Power ministry X. Okay So why close to zero and x equals to zero. We will use these two conditions seven plus E two equals to zero your question first and seven U. to the power for Plus You two into the power monastery calls to move on. seven is U. to the Power three. Mhm. by solving these two conditions Stephen is E to the power three upon the power seven money is one. This is a seven. By calculating it. We will get it. Yes it will be months of U. To the power three appointed to the power seven man istvan. So now we will put those values here. So why even will be equal to U. To the power three upon it. To the power seven minus one. To the power for X plus. Mhm. Mhm. Into the Power Monastery upon you. Two months of to the power three to the power seven minus one. You did the part ministry X. Mhm. So what he calls to solution very close to Yeah U. To the power three upon U. To the power seven Man is one that is U. to the power four X minus of will do the Bartman itself three X. So this is now answer. I hope you understood. Thank you.

Hello. We have to solve the given differential equation. Find a political solution for this. Given differential equation for the scurvy monastery very close to zero divide. Is to advice for When x equals two zero. So we can add auxiliary equation four. I miss carmen is m equals to zero. Mm. That is four M minus one. That is because 20 M will be zero and 1 Way four. Okay. Mhm. So when it comes to solution believe very cool to see even U to the power zero x proceeding he did the Pavlov X wait for. So this will be called to see even plus see to it the power X way for. Mhm. Device to advise for except close to zero. Actually close to zero by given four question and if I will be device to Yeah never will be. So you too bye four. Because to society will be hate. So Steven will be 4 -8. That is -4 solution will be why Cause too it into the power of X. Y four minus four. So this is the answer. I hope you understood that.

First we can divide both sides by Y squared notes that the left hand side can be re reading us the cancel worldwide, and the right hand side can be reading us de Artes Y. And now we can integrate both sides. We know that exceed goes to when Y equals four, so to over four. Because eight plus C and has C. equals miners pure up over two. So the answer is exa, World Y equals X. Y, miners 12/2.

In this question we are given with the solution of the differential equation. So the deferentially commission given to us is day into wild ish. E listen to the way Here he goes to zero and the solution I think you want to us. Yes. Why is it was to see three days to the power -3. So let us start with the solution. I am going to differentiate about stay here so see what happens. We get here. Day, bye bye duties. It was too Say into -3 into theories to the Power -4. Now we are going to multiply by a year. So after multiplying by T on both sides, you can see we get their T into nearby by did it goes to minus Tracy Give us to the power -3? No, we are willing to use this equation one. So I'm going to substitute the value by the equation one. So after using the equation one here, we can see we got here T into day, bye bye dating as it goes to minus Tracy. Sorry, -3 into why and no, after simplifying it, we can say that finally it can be written as stay into wild Dashti last three wide, it goes to zero. So this is that required differential equation. What is given question? Okay, thank you


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