Problem

$x^{3} y^{\prime \prime \prime}+x y^{\prime}-y=3-…

05:31

Problem 20 Medium Difficulty

$\begin{array}{ll}{x y^{\prime \prime \prime}-y^{\prime \prime}=-2 ;} & {y(1)=2, \quad y^{\prime}(1)=-1} \\ {y^{\prime \prime}(1)=-4 ;} & {y_{p}=x^{2} ; \quad\left\{1, x, x^{3}\right\}}\end{array}$

Answer

$$
y(x)=2-x^{3}+x^{2}
$$

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Calculus 1 / AB

Fundamentals of Differential Equations

Chapter 6

Theory of Higher-Order Linear Differential Equations

Section 1

Basic Theory of Linear Differential Equations

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Video Transcript

Okay, Look at the question 29 that is using the question. Trains not says book. You will see that engine. A solution is given us y of eggs equal to y particular which in this case, is X squared them plus c one more tip led by one which is the first element in the sides lost seats you mort supplied by eggs. Loss it, Terry. More supplied by X cubed. Now I want to find a solution that satisfies the given initial condition. No, of wire off Warne in this case will be Also wants word lost one lost seats. You blossom, dearie, we have, that's why warn is the court too soon messing them this question one? No, we are now when it's a cop, it's white prime of eggs. So white prime of eggs When different shit that you have two eggs loss. It's you lost three c three x squared We have that's wide prime of one we call soon minus won't. So this implies that minus won't record. So plug in, Won't you gonna have you loss? It's laws three c three lesson in this equation to next, we need to calculate its wide double prime of eggs when a different ship this young soon lost 663 eggs, no abducts wide prime time off alone because of minus four, travel is minus four quarto. Assume lost. 663 That implies a 663 equal to minor sings on incident. Very important to minus one. So this is one of the solution. Now we can plug and see the reading. Interesting question. Suits you get six. Ooh. So flog sit Cherie into equation soup. You are so lost Q minus three quarts of minus one. This implies that seat to record. So zero Lastly, less blown seats. You on C three into the equation. One you're gonna out that C one equal to two minus one plus one. This implies that C one according to Sue. So I got him. I see one on seats. Sue on sitter damaged on y of eggs will be called X squared Loss C one is too on the century. Zero I'm considering is minus one minus x cute. So this is the answer

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