are-the-following-differential-equations-linear-explain-your-reasoning-fracd-yd-xx2-ysin-x

Question

Are the following differential equations linear? Explain your reasoning.
$$
\frac{d y}{d x}=x^{2} y+\sin x
$$

Prathan Jarupoonphol · Accepted Answer

high in this video, we are going to deter my weather. This differential equation is linear d y by the X equal x square wide plus Sign a base now for first order or the E When you want to check if it is linear, you try to arrange it into this. Can&#x27;t equal a phone. Why Prime plus p of X y Equal kyo picks where p and Q Here are functions on lian eggs. So no, why involved? If you can do this, we can say that the equation is vigna in this question we have Why prime as usual And we can move X square. Why? To the left eye and leaves I&#x27;ll x there and we can have minus x square our p of x sile X s R q of eggs. That means our equation is in fact, linear because it can be arranged in such a way on Dhe. This is it. Thank you.

Prathan Jarupoonphol · Answer

in this video, we are going to deter my whether this differential equation do I buy the eggs. Plus why square equal eggs is linear or not? Ah, if you are familiar with this kind of question, you can see right away that we have y square here. So is not linear. Because why is our, uh, function that we gonna so far and to fight to be linear? It had to stay at most at the B one, but to give I&#x27;m all concrete reason resenting you No. Do you show form that we go to when we wanted into my weather or the is linear And if or the cannot be arranged into this form then it&#x27;s not linear. Our question has why prime plus why square equals eggs. If you want to compare this to you, have wife Ron ask you So you have a queue of X which is our ex because there&#x27;s no is a term with no why involved now the last term door Pio X y cannot possibly equal y square because West craze Why times Why even every match this why together you used to how this why I left and it cannot B p of X, so it cannot possibly be arranged in such a way. So it&#x27;s not linear, that is it.

Robert Daugherty · Answer

Section four, not five. Problem to 11. I&#x27;m ask, is the differential equation that you see here Is this a linear differential equation? So the form is going to be why prime is equal to sorry. Why prime plus a function p of x times Why is equal to a function Q of axe. So, yeah, I can see this. In this case, if P of X is equal to zero, and cue of X is equal to X cubed plus e to the X, then, yes, this is a linear differential equation.

Prathan Jarupoonphol · Answer

high in this video. We are determining whether this equation why prime? Because why plus e to the y is linear or the owner. So we know what to do. We go to our usual form that we used over and over again and try to arrange our equation into this every can. Then it is linear. If it can&#x27;t, then is not. Now we have, uh, move wide to the left side and leave it to the white. There, you can see that the second term, our p off X is just minus one, which is fine. No problem there. We have a problem on our last term, though this two cannot mash because q of eggs We wanted to be function solely on eggs. No. Why wolf? And here we have just e to the y. So it is clear that it cannot the Huo Biggs. So we conclude that this equation is not lenya because we cannot arranged it in such a way. And that is it. Thank you.

Robert Daugherty · Answer

section 4.5 Problem to a nine. I&#x27;m looking at a different equation. My question Is this a linear differential equation? So if I can write it in the form y prime, um, for me So why Prime Plus and I can write some p of X and sorry. Let&#x27;s back up our variables t so p of T. Tom, why is equal to Q of T if I can write it in this form than it is a linear equation, so I could rewrite. This is D Y d t minus T Y is equal to zero, so you can see I can write this in standard form for a linear equation. So this is a linear first order and differential equation. Ordinary differential equation.

Alexandra Embry · Answer

in this problem. We want to decide if this is a linear differential equation or not. And to do so, we want to check each term and decide if the coefficient of the term is a function of X on Lee. And if it&#x27;s equal Teoh a function of X only. So we see this term is okay. This term is linear in terms of the third derivative of why this term is linear in terms of the second derivative of why this term is linear in terms of the derivative of why? Because this sign of X only contributes is a function of X. It&#x27;s not a function of why. On the other hand, over here we have a function of why here and so we don&#x27;t want any functions of wide to be the coefficients of any of our why or derivative of why terms. So this prohibits our equation from being linear, and so therefore, this is not a linear differential equation.

Problem

Are the following differential equations linear? …

Problem 208 Medium Difficulty

Are the following differential equations linear? Explain your reasoning.
$$
\frac{d y}{d x}=x^{2} y+\sin x
$$

Answer

Linear.

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