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The method of undetermined coefficients can sometimes be used to solve first-order ordinary differential equations. Use the method to solve the equations.$$y^{\prime}-3 y=5 e^{3 x}$$

Calculus 3

Chapter 17

Second-Order Differential Equations

Section 2

Nonhomogeneous Linear Equations

Johns Hopkins University

Missouri State University

Harvey Mudd College

University of Nottingham

Lectures

04:29

The method of undetermined…

01:35

01:21

06:34

06:55

01:23

01:41

03:56

Use the method of undeterm…

04:33

13:35

Solve the differential equ…

02:20

03:24

this equation. Why? Crying minus why it's called too life today, three X. So we're gonna try to use the method off on determined politicians to solve it. Um, on the turn conditions. So you have these, but I'm a genius equation corresponding, or you know, no will be. Are minus three for a solution on the form the our next. So we have these. Will we see that, you know, is that are moving that over there is hostile people to three. So hey, Eatery three x is gonna be a solution for the on what? Genius equation G wise. Each no sees things coefficient. The three x appears also there he was those, uh well, was that that solution? Let's assume that is gonna be some A eggs. Hey, Time, sex times You did it. Three x. Um, since we have the right thing there, perhaps of years to be something like that, So Well, let's see what happens. You have that for our articular solution. What happens if we differentiate this solution? We're gonna have differentiating first decide. So just a times you three x now are differentiating this site. The with the ex. You're a X stands. Three either. Three eggs. So this is why Brian Blunden make you satisfy the situation. So we would plug in. Ah, replace for why is well, Brian, I'm being too that Greece obstruct three times why we're gonna have, um why France p will be OK. Three x plus a X that was three. So three a x g x my nose three times. That's my honestly and say, X beauty three necks that has to dio to five three x And so sees these these, uh, part souls homogeneous equation these that accept these to cancel. And so we we have that these has to be voted that sees the functions are equal. These coefficients, they're all someone's vehicle. So from that, you know that has to be able to fight. Um, so that our article our solution is you have to go through by times X never ceded it to you. Thanks. On the gym, the only genus solution would be that so that there are general solution. Would be, uh, would be this part the particular five x three x five x eager three X plus some constant TMC to three x Yeah, three x so these art is a solution to rip articular equation. This is the homogeneous solution. So this general solution will be the some of those.

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