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Solve the system of DEs below:(D-1)x + 2y = etDx +D'y = 0...

Question

Solve the system of DEs below:(D-1)x + 2y = etDx +D'y = 0

Solve the system of DEs below: (D-1)x + 2y = et Dx + D'y = 0



Answers

Solve the differential equation.

$ y'' - 6y' + 9y = 0 $

In this problem, we have to solve the differential equation. Why? Double pane plus two y is equal to zero. Now we can associate the characteristic a creation. Tow this to function invasion which will be given by t squared plus two. Is it called Tuxedo? Now let's recall the Purim when we have the complex route off, the characteristic decoration puts this. So this is theory and 11 from the textbook. If the roots looks like Alpha plus I beata on our two is a call to Alfa minus. I better are the routes off the characteristic in creation, then the solutions or in general, solution is going to look like Why is he called to Ito the poor Al Fix times. See one times co sign off Beat X plus Tito time Sign off, be takes. So we're going to use this to solve this problem. So now D squared. Is it going to negative too? This implies TZ called too plus minus square root off I So that means my Allah phrase he called to zero and beat Isaac called The Squire rode off to so then the general solution off this differential equation. It's going to be. Alfa is zero and Ito Depot zero is indeed, it's a call to one. So see one times Co sign beater betide square root off two times six plus C. Two time sign off. Squire rode off to X, so there's going to be our final answer.

We want to solve a given differential equation which states why square D X plus dy is equal to zero. This question is challenging our ability to solve differential equations in particular. It's challenging our ability to use integration methods in conjunction with our newfound method for solving separation of variables. The separation of variables method requires three steps to execute. First. We're going to isolate X and Y on either side of the equation, so push Y terms the left side of the equation. X turn to the right secondly, will integrate both sides of the equation because each of the equation has a differential enabling us to do so. Thirdly will evaluate each integral integral methods to solve so first isolating X and Y. We have won over Y squared dy equals negative dx integrating This means integral dy over Y squared equals integral negative dx. The right hand side is something negative X. And we have to include a constant of integration. So our solution is negative. One over Y equals negative X plus C. The constant of integration.

Hello. We have to solve the given differential equation that is G. T. Y. Please develop breast away. It cost a hero. So. Exalted form of the seclusion and mr plus M press to cost +20 So the complexity of this will be minus B. Plus money. Scuttled off one monies for into into one upon to. So this will because two miners of one x 2 plus minus. You squirreled off 78 upon 12 ι.. So alpha is one way to beat is square root of seven. So the solution can bitterness into the power of Halifax Stephen cause she went side we tax plus you do cause be text. This is the solution. So this will be cause to the to the power minus X. Y. Do seven off sign Beat. ISAT scores out of seven x 2 of X. Plus. She too calls scurried off seven x 2 or Fax. So this is the and so I hope you understood.

Hello. We have to solve the given differential equation. That is two of the survey monastery device. Man is very close to zero. So we can add the actual education for this to end this car Ministry. M Man. It's funny quest to zero. This is the use of the equation. Okay, so we can solve it to m squared minus off today minus 12 1. So root of this object. Education will be three plus the route 17 x four. Mhm Yeah. Yeah. M two will be three manages current of 17 upon four. Mhm Okay. Yeah. Okay. So we can write down solution for this given differential equation. Okay, so this will be cause to white cause to see even into the power and Monex plus you took you to the Pavlov mm two X. So when it comes to seven into the Pavlov three plus the square root of 17 upon four or fax AC two into it. To the power of three months is square root of £17.4 of X. So why will be constant into the power three by four is three X of I four is common. So this will be into the power route 17 upon seven into a. To the power of 17 upon four of X. Please sit into Italy power minus office to carry out of 17 upon full. It affects. So this is that answer. I hope you understood. Thank you.


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