5

20y1:y(0) =14 (0) =3...

Question

20y1:y(0) =14 (0) =3

20y 1:y(0) =14 (0) =3



Answers

Solve the initial-value problem.

$ 4y" - 20y' + 25y = 0 $,


$ y(0) = 2 $,


$ y'(0) = -3 $

We have an equation. We have to solve the situation. So this is 1/4 order equation. So we can substitute for Why my square equal to X. Then we can rewrite the questions five X squared minus seven X. Plus 1.5 equal to zero. This is a corporate education. So we can solve for X. Using the corporate form lex equal to minus as a minus of this guy. 49 -4. and do five do 1.5 Like two times 8. That is equal to seven plus 49 19 right 10. He said that this X can have two values. It's gonna do seven plus 19 10 4. I think we're too seven minus 90. Like now are by square is X. Y. Then we can write by equal to rope eggs. So we can have two values for each extra and extra. That is why weren't you going to less or minus? Excellent. Difficult to english. Why even equal to seven plus. So 19 x 10 or write to it too? Pro Text one is here or minus route seven this 19. All right, then, Or four x 2 x three equal to plus seven minus Group 1910 or my for equal to -7 -19. Right. These are the four possible solutions of the Give any questions.

So are asked to justify each one of these steps. So here, from this step here and we'll use it for color, you can see that we have gone from a 15 white 1 25 So basically what's happened here is we've added 20. Why to both sides. So that this done cancels out and become zero here. And the 15 plus a 25 is 35. And so this is just the addition property, because you can add the same number and remember a wise just some number. So 20 times that number is the is just some number. And when we add it, we added to both sides and that's your addition property. And then this next one here we've subtracted seven from both sides. And so this cancels out to zero here, and this 12 minus seven is a five here. So that's just our subtraction property. And then when we divide both sides by 35 and divide here by 35 this becomes why, by itself cause thes cancel and we can reduce this five over 35 to 1 over seven. And this is the division property

Yeah. In order to solve this equation, since it's already in factored form, we're going to take each factor and set it equal to zero so three y minus five equals zero and Y plus seven equals zero. Now we just need to solve each of these so we'll start by adding five and then divide by three. So our first solution is Y equals 5/3, and then our second solution, we get Y equals negative seven. And as always, these answers can be verified by plugging them back into the original equation for the Y values.

So for here. If we're solving for why in the equation Explosive five. Why's he going to 14? I'm going to start out by subtracting extra boats. As of my equation. To get five y is equal to 14 minus X because these components cancel up from here. I just have to divide boats, as in my equation by five, and that gets rid of the fives. And now my why is isolated and it becomes 14 minus X.


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