determine-the-values-of-the-constants-r-and-s-such-that-ix-yxr-ys-is-an-integrating-factor-for-the-2

Question

Determine the values of the constants $r$ and $s$ such that $I(x, y)=x^{r} y^{s}$ is an integrating factor for the given differential equation.
$$2 y\left(y+2 x^{2}\right) d x+x\left(4 y+3 x^{2}\right) d y=0$$

Sajin Shajee · Accepted Answer

Okay, I x is equal. I eggs comma wise equal to x are Why? As so then this is a case and you have to Why? Why? Plus two x where X plus x times For why three. X He won huge X are why ask plus one q x squared like the axe was extremes are puts one Why I like the symbols like three x squared For I 18 em is equal to x r em is equal Teoh four times x r plus two plus like the s plus two and equal to three time actually are plus three life as clothes four times X d art was one old but like the s plus one see and then derivative four x y plus, but by why as post plus one here. So then we do partial period in terms of first partial m partial impartial Why is equal to q X? Are y as multiply too a few tens s plus one multiple x a second plus two plus as multiplied by why partial and up are still acts would be equal. Teoh x are why s three times are plus three x squared most four times are plus one. Why so then we still see each of them equals two times rearranges Probably when you said these two equal to each other, it will be four times as plus one multiplied by X square plus a few times as plus Q by people three times are plus three over X where of four times are one Why? So we have four times s plus one is equal to three times are pushed The read she and then be a two times best plus two which is equal to four time are plus one s finest Three are equal to five que s to s minus four R&#x27;s equal zero ass is equal Teoh So are so. Then it will be e s minus three weeks. They&#x27;re not as our means. Three r is equal to find r is equal to one and s is equal to two So then I, uh x com Why will be equal to x times y square? This is the integrating factor

Problem

Determine the values of the constants $r$ and $s$…

Problem 31 Hard Difficulty

Determine the values of the constants $r$ and $s$ such that $I(x, y)=x^{r} y^{s}$ is an integrating factor for the given differential equation.
$$2 y\left(y+2 x^{2}\right) d x+x\left(4 y+3 x^{2}\right) d y=0$$

Answer

$I(x, y)=x^{1} y^{2}$

Related Courses

Differential Equations and Linear Algebra 4th

Related Topics

Discussion

Top Calculus 2 / BC Educators

Grace H.

Heather Z.

Caleb E.

Samuel H.

Calculus 2 / BC Courses

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Watch More Solved Questions in Chapter 1

Video Transcript