Problem

For the following problems, find the solution to …

03:21

Problem 276 Hard Difficulty

For the following problems, find the solution to the initial value problem.
$$
(x-1) y^{\prime}=y-2, y(0)=0
$$

Answer

$y(x)=2 x$

Related Courses

Calculus 2 / BC

Calculus

Chapter 4

Introduction to Differential Equations

Section 5

First-order Linear Equations

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Video Transcript

this video. We are going to solve the problem off solving this equation. Why? Prime times X minus one equals Why minus two. And we also how initial conditions saying that why off zero is zero now, this can be so abusing separable off separation or variable. Right? So we moved. Why here? And move takes to the artist's eye eggs. And luckily, these polynomial can be integrated like once there and done so we help love. Oh, why Venice too Equals of X minus one plus some constant. I skipped one on two. Step here involving changing. Changing the why into the off deal. Why? Minus two and shin the X here to the off X minus one, but is very simple. And you should be able to do it. And here we are at this step, we want to We don't want why two stuck inside lock elated. We won. Why? As a function of X. So what we can do is we We use both sides as a power off e because we won lock to disappear. We power power over easy, and we gonna this gonna can So the locker is, um we have y minus two equals X minus, one times E to the C this constant. And we can eliminate this because now we have in the show condition. Right? So why off zero when X is Ciro, Why will be zero? We have zero minus two equals, Ah, serial mass one times times e to the sea. So this is gonna tell us that what ever sees you needed to see as a whole equals to two, right? Essentially See, is lot off too. But never mind. We just want these. We plug it back in here, you're gonna have why? Mine has to equals two eggs, minus two, and we cued and minus two. We have. Why equals two ex asked our particular solution for these questions. And that is it. We can you see the shape that if you pluck this back into the initial Odie, we're gonna get that is satisfy the creature. That is it. Thank you.

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