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Problem Kol,25 points: Soive the fo lowing diflerentae equation witn x (0) 0;x(0)...

Question

Problem Kol,25 points: Soive the fo lowing diflerentae equation witn x (0) 0;x(0)

Problem Kol,25 points: Soive the fo lowing diflerentae equation witn x (0) 0;x(0)



Answers

$y^{\prime \prime}-(\tan x) y^{\prime}+y=0 ; \quad x_{0}=0$

In this question we are going to solve the equation, X Plus one is equal to zero. So what you do in this question is that what you whatever operation that you do on the left side also do the same on the right side. So here we want the value of X. So we want to make X the subject of the formula by removing one from this side. So the next step is X plus one -1. But what you do on the left, you also do on the right. So we have 0 -1. And on our left side we now have X plus one minus one. So these ones uh minus each other out, then we have X is equal to 0 -1, would get my next one. Therefore our solution For this equation is X is equal to -1.

First we want to solve for this problem, working acts equal to equal zero. If we go back to our absolute value rules, we know that absolute value of zero equals Europe, so X has to equal zero.

Hello. We have all the number five questions is solve the question. Okay we have to find the Halifax basically determinant is X. Plus A. X. X. X. X. Plus A. X. X. X. X. Plus a. Equal to zero. So let us just ah operate are one are one place are to place are free so this will become Explosive Explosive. three x plus A. three x plus a. three x plus a. X. X. Plus A. X. X. X. Express A. Will be able to zero. Now let's take three explosive common. We'll be left with 111 X. X. Plus A. X. X. X. X. plus a equal to zero. Okay now we have to operate to get uh get 1002-0 here. So we'll be operating C. Two C. To minus C. One and C. Three C. 3 -1 1. Okay So three x bless a Si Tu -7. So C. One will be as it is one xx zero A zero 00 Okay And it should be equal to zero. Okay? It implies three express a. Into that is operate like this. It's quite equal to zero. So three x plus equal to zero X equal to -3 x three is the only solution. Thank you so much.

Our goal for this problem is to find a problem that has a quadratic function and it has a vertex of 00 So if we know the vertex 00 that means that you will have something like y equals x squared um like this. Um and then there won't be another component of the component because that would mean that there would actually be, if there was a bi component then there would be a vertex. So it's just going to be an x squared term. And we know that when uh x is 25 for example, we have 25 squared, I would be 6 25 and we wanted to be 1 25. So if we use 6 25 divided by 1 25 we see that that's five. So we want to make this 1/5 X squared. So that way when we look at X equals 25. Yeah, we see that it intersects here at 1 25. So therefore we found the equation of a quadratic function that has a vertex 00 Um and it passes through the 0.25 125. So we solved this problem.


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