write-the-following-first-order-differential-equations-in-standard-form-fracd-yd-t4-yt-ytan-t

Question

Write the following first-order differential equations in standard form.
$$
\frac{d y}{d t}=4 y+t y+	an t
$$

Prathan Jarupoonphol · Accepted Answer

high in this question. We are going to arrange this equation into standout form. Divide by T ea quo for why? Plus tee off. Why? Plus 10. Oh, tea. Hear t is free. Variable like eggs. In other question, it just changed the name. Nothing complicate their, uh I understand art form. It means this foam Ah, here will be p r t instead off p of x equal Q Off T and let&#x27;s do it we have Why, Prime, As you show now, we move the term with why to the left side and it&#x27;s gonna be my nest full. Why mine s t y? And we left tens of tea on the rice I And here we removed. We pull. Why? All of it is going to become minus four plus t times. Why? And he&#x27;ll be how our equation. You understand that form where minus four minus t gonna be P O. T. And 10 of T s Q r t. And that is it. Thank you

David Elzinga · Answer

in our problem we meet must take the first order differential equation. Why prime equals execute y plus sign of axe and write it in standard form. The beginning part of this problem is to recall that center for minutes I&#x27;ve labeled it in green. On the right hand side, zoom us up. Here is white crime by itself, plus p of x times y on the left hand side equals Q Becks on the right hand side. So let us inspect how our equation matches or does not match this form. So beginning. Let us notice that we desire to have y primed by itself on the left hand side. And indeed, that&#x27;s how did Piers now? So our goal will be to not manipulate this term. Next, we need to have all the terms and involved Why in a linear fashion on the left hand side, I say linear fashion just means why to the first power. So which terms over here involved wide in the first power? Well, this term right here involves wide of the first power in a sign of X dozen. So I want to get all the terms involving Why did the first power on that left hand side. So let me move it over minus X cubed. Why? Equal sign of acts and then next notice. I want y prime plus p of x y so I can rewrite this and a little bit of way that&#x27;s more matching of standard form is I can write it like this. I just putting plus and then the negative just wipe aren&#x27;t plus Snegur execute. Why? Equal sign of X And now here you can clearly see what p of X is p of X. Is this term right here? So we have got all over than your terms involving. Why in the left hand side and next. You know, um, of the terms not involving, why just acts on the right hand side. And indeed these the sign of excess only terms not involving why or why prime for that matter. And it&#x27;s on the right hand side by itself. So this right here is our final answer. The box it and we are done

Prathan Jarupoonphol · Answer

high in this question. We are asked to arrange this equation. Why? Prime plus three y minus lots of eggs equals zero into the standard form he had to stand up for mean. Ah, the sand art form for Lena. First order equation. So we just move lock off base here, and we gonna have our equation into this form. The form that we go to every time we shake. Whether something is Lena, that is the standard form. And we have tree as p of X lock eggs as cure picks. And that isn&#x27;t Thank you.

Robert Daugherty · Answer

section four out 5 to 15 were asked to write this different equation in standard form. So keeping in mind standard form is gonna be why prime plus some function of X times Why is equal to some function of X? Okay, so in my case, if I take this equation, I can write this as negative x y prime plus it&#x27;s with me minus three X plus two. Why is equal to X E to the minus X. Now I want this. Why Prime to be by itself, I could divide the entire equation by ex just would say negative X so I can Why Prime is equal to and this is gonna be minus three X plus two over minus X. Why is equal to minus E to the minus X and so I can simplify here than negatives were gonna go away. So this is sorry about this. This is a y Prime. Keep making this mistake right here. So you get it&#x27;s gonna be a wide prime plus three x plus two over X. Why is it about a minus? E to the minus X

Smita Praharaj · Answer

in this question, we asked to find the order of the differential equation. Divide over. DT equals to t Let&#x27;s recall that the order off the differential equation is the highest order derivatives in the equation. How do we determine the order off the derivative? So if we have y prime or Sadie, we were d T that has ordered one. Why double Brian on the Square y or Petitti Square? That has ordered to Why Triple prime are the tree by over D D Cube that has ordered three and so on. In this equation, we just have one derivative that is D Y over DT, which has ordered one. So the highest order is also one. So that&#x27;s the order of the differential equation.

Clarissa Noh · Answer

it&#x27;s clear sailing. You married here? So what we have to first do is different sheet Will sides from our given So yet the derivatives equal to one plus t eats the why we need to find the unnatural condition you make x be cool too negative too. And for why? Negative too. We get negative two plus floor won&#x27;t agree from negative to negative, too. T e T o r i a t Do you thi we know that this goes to zero So the answer is people to to

Problem

Write the following first-order differential equa…

Problem 216 Medium Difficulty

Write the following first-order differential equations in standard form.
$$
\frac{d y}{d t}=4 y+t y+\tan t
$$

Answer

$\frac{d y}{d t}-(4+t) y=\tan (t)$

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$\frac{d y}{d t}-(4+t) y=\tan (t)$

Calculus

Grace H.

Kayleah T.

Kristen K.

Samuel H.

Integration Review - Intro

Definite vs Indefinite

Gilbert Strang,Calculus

Grace H.

Kayleah T.

Kristen K.

Samuel H.

Gilbert Strang,

Calculus