Question
Question 4Same Instruction as QuestionSolve linear homogencous equatlan (real solution}Y'+6y 8y = 0Use the editor t0 formiot your onswerQuestion 5Some Instruction QuestlonSolvu Ilnear homogeneous cquation (real solulion}8/ + Z0y =
Question 4 Same Instruction as Question Solve linear homogencous equatlan (real solution} Y'+6y 8y = 0 Use the editor t0 formiot your onswer Question 5 Some Instruction Questlon Solvu Ilnear homogeneous cquation (real solulion} 8/ + Z0y =
Answers
In each of Problems I through 8 find the general solution of the given differential equation. $$ y^{\prime \prime}+2 y^{\prime}-3 y=0 $$
So yeah, we have y squared the eggs gloss to x y los co sign wide Do Why equals zero. I write this as Sue X Y Law School sign. Why do Why equal to minus y squid DX? This implies that Dwight the eggs equal to minus y squared over two x y los co sign Why? So we can see that this is not separable Because you can't write these cancer rides as f of eggs? G of why? So this implies that's it is not separable. Next we check to see if it is linear. You can see also that it's cancer Bolena. So it is not linear. Why? Because you can't write seeds. You can't arrives as a one of x d Y d x Plus is your off eggs off? Why records would be of X. So it is not Vigna. Now let's see if it is exact from the equation. Won't we can see that our am off x come Why equal to y squared on our end off x camera? Why Equality sued Su ex wife Blasco. Sign of Why So this implies that's d m do I? It halted. So why? Under ndn D X equal to two. Why also So this to our equal. So this implies that it is exact.
In this video, we're gonna go through the answer to question number seven from chapter 2.4 so as to show whether this equation inseparable, linear or exact or none of these. Okay, firstly, is it separable? It's quite clearly not because you condone you're just never gonna be able to split up this cause x y or this calls ex wife into a function of X times. By a function of why you just never gonna be able to see that So is not separable. Is it linear again? It's not linear because cause of X Why is a nominee a function of X on dhe? A moment of your wife is exact. Well, let's see. Let's try and work out What gm the wise when M is this guy? Eso differentiate that inspector why we used the, uh, the product rule for the second term. Okay, so that's gonna be because x by close. Why? Times x AA minus at times my minus sign specs. Why? Okay, so let's just go through that. So, firstly, we different rate the at the y on left cause X y alone. Then we left. Why alone on different trade cause X Y ah, we do the chain with your friend shake cause that's why that's why we bring the X out the front and then caused different shades to my side. Okay, so this is cause thanks. Why? Plus rooms minus next. Why sine x y Then let's see whether that's equal toe the end The X Where is the commission Off the d y in the equation. So again, using chain rule? Yeah, it's gonna be cause text. Why minus, Let's see X times Why times sine x y that's using the chain will once again Okay, so the M d y is equal to the MDX, so therefore, it is an exact defense in question.
In this video, we're gonna go through the answer to question number one from chapter 2.4. So ask to classify whether the equation here is inseparable, linear, exact or none of these. Okay, First, let's, uh, see whether it is separable s O. If it's separable, then we can write it as some function. G off X times by D. X plus some function Hey, age of why times by d Why equals era? Uh, not clearly. We can't do that. Yes, we can put this X on this side, but there's no way Thio put this. Why? On its own? Ah, on this side. Because we basically have a term containing why Aditya term not containing why so you can't base put those two up. So it is not several isat linear. Ah, yes, it is linear. That's because you condone, um quite easily Write it as, uh let's see to it, right Asked me why t x, um minus X. Why is equal to X gives minus one of eggs? Why? I mean minus X Cossacks on this is in the form needed to be linear, as in there's only terms continued. Why? Andi want Jax Thanks. So it is Lydia. Uh, that is exact. Well, let's see. So Well, let's look at the M, the md. Why? So this is day 50. Why, off the first term, which is X squared y plus extra for cause X won't write that down. You could see that from the previous page, but the wide derivative is gonna be X squared. Uh, let's look at the end of the ex. This is minus X cubed. So the ex relative of that is gonna be minus three. Next squared. These two are equal to each other. Therefore, this equation is no exactly.