determine-the-order-of-the-differential-equation-yprime-primex-yprimeex-yyprime-prime-prime

Question

Determine the order of the differential equation.
$$y^{\prime \prime}+x y^{\prime}+e^{x} y=y^{\prime \prime \prime}$$

Michael Jacobsen · Accepted Answer

let&#x27;s consider the following differential equation. We have the second derivative of why, plus independent variable X times, the first derivative why plus either the x times the function why itself equals the third derivative of why a road to find the order. We simply must determine what the highest order derivative is the problem from the first trim we have the second derivative in the second term. We have a factor that involves the first derivative. And then when we go across equality, we see that the right hand side involves the third derivative. Therefore, the answer to this problem is that this is 1/3 order differential equation.

Hira Saeed · Answer

Here we have to find the order of the differential equation. This care by by the exterior. Mhm. This sex DVD body X. This guy is equal to E. Exponential X. Mhm. So by definition, the order of the differential equation is the order of the highest order derivative in the equation in this invasion, divided by DX, is the first order derivative, and this cave by by DX cure is a derivative of the second quarter, mm hmm. Therefore this is the second order differential equation. Therefore this is the second order differential that vision.

Michael Jacobsen · Answer

consider this following differential equation, but we would like to do is determine its order. So let&#x27;s go turn by term and find the order of each derivative that&#x27;s present in the first term. We have the second derivative of the function Why trapped inside the sine function. So here we have the second derivative. Then we have the defendant variable squared times, the first derivative so first arrived in the second term. Here we have just the ordinary function. Why itself? And there&#x27;s no derivatives on the opposite side of equality. So the order of the differential equation is the highest order derivative that appears, and we could make the following conclusion. The order is two. In other words, this is a second order differential equation.

Smita Praharaj · Answer

so he really has to determine the order of the differential equation. Why Triple Brian Plus why double prime times why Prime equals +23 x squared. The order of a differential equation is the highest order derivative in the equation. For example, if we have by Prime, that&#x27;s the first derivative size order one my double prime has ordered to by Triple Prime has only three and so on. Now, in this problem, we have a bunch of derivatives. So we have Y triple prime that has ordered three. Why double Brian? That is under two y prime that has ordered one. Now the order off the great differential equation is going to be the highest order derivative here at the highest order. Bit of his three. So the harder of the differential equation is three.

Taylor Shimono · Answer

so to determine the order of this equation, we essentially want to determine what is the highest power derivative that we have here. And so we see that we have a why with no derivative. So that&#x27;s not going to be a high order. But we also have a Y prime in a white prime squared. So the Squared might make this a little bit trickier because we might be tempted to say its second order. But because really, it&#x27;s still the first derivative that just tells us that our highest, a derivative, is going to be one, so we have a first order.

Michael Jacobsen · Answer

in this problem, we have an ordinary differential equation for which we&#x27;d like to determine what its order might be. In order to find the order of the differential equation, we first looked to see what all of the derivatives are. Here. We have the first derivative D Y T X of the function. Here we have the ordinary function itself to the power of to and here we have an expression involving the independent variable X. In this equation, we might determine that the order is three due to the outer exponents three. However, that would be a trick on this problem, since only derivative is the first derivative since only the first derivative is present. This is a first order differential equation. Think to note on this problem. If we did have an expression of the form d three y dx three, then this would have indicated 1/3 order. So this is a caution to watch out for another, further problems

Problem

Determine the order of the differential equation.…

Problem 3 Easy Difficulty

Determine the order of the differential equation.
$$y^{\prime \prime}+x y^{\prime}+e^{x} y=y^{\prime \prime \prime}$$

Answer

3rd-Order

Related Courses

Differential Equations and Linear Algebra

Related Topics

Discussion

Top Calculus 2 / BC Educators

Grace H.

Catherine R.

Anna Marie V.

Kayleah T.

Calculus 2 / BC Courses

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Watch More Solved Questions in Chapter 1

Video Transcript

Stephen W. Goode, Scott A. Annin

Differential Equations and Linear Algebra

Grace H.

Catherine R.

Anna Marie V.

Kayleah T.

Integration Review - Intro

Definite vs Indefinite

Additional Mathematics Questions

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

3rd-Order

Differential Equations and Linear Algebra

Grace H.

Catherine R.

Anna Marie V.

Kayleah T.

Integration Review - Intro

Definite vs Indefinite

Stephen W. Goode, Scott A. AnninDifferential Equations and Linear Algebra

Grace H.

Catherine R.

Anna Marie V.

Kayleah T.

Stephen W. Goode, Scott A. Annin

Differential Equations and Linear Algebra