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TuringTest
 4 years ago
y"+y'=3x^2
Can someone explain why, if we use undetermined coefficients on this, we need to guess that Yp has an x^3 in it ? I can't seem to find the rule about this.
TuringTest
 4 years ago
y"+y'=3x^2 Can someone explain why, if we use undetermined coefficients on this, we need to guess that Yp has an x^3 in it ? I can't seem to find the rule about this.

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Mertsj
 4 years ago
Best ResponseYou've already chosen the best response.0Isn't it only sensible that if a sum of two derivatives has an x^2 that the integral would have an x^3? Or am I being too simplistic?

phi
 4 years ago
Best ResponseYou've already chosen the best response.3the problem is the homogenous solution contains a e^0 i.e. a constant, which matches one of the derivative of the righthand side

Mr.Math
 4 years ago
Best ResponseYou've already chosen the best response.1Assume you have some polynomial P(x) as as solution of the given differential equation. Now, the given DE indicates that the sum of the second derivative added to the first derivative gives us a second degree polynomial. That means our assumption should be a polynomial at which its first and second derivative contains a term of x raised to power 2. Does that make sense?

Mr.Math
 4 years ago
Best ResponseYou've already chosen the best response.1In other words, adding the term with x^3 so that we will get x^2 for y'.

phi
 4 years ago
Best ResponseYou've already chosen the best response.3if you had e.g. y'' + y' +y= 3x^2 then the particular solution would be order 2

Mr.Math
 4 years ago
Best ResponseYou've already chosen the best response.1Yes, if we had y in there. But since y' has the largest degree, then it should be of a degree 2. (y' should have a degree 2).

lalaly
 4 years ago
Best ResponseYou've already chosen the best response.0i explained on the other post Turingtest, please go check it when you see this

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.0im curious that since the derivative of a function IS a function; why we shouldnt be able to play with this as a: y' + y = 3x^2

amistre64
 4 years ago
Best ResponseYou've already chosen the best response.0is that possible? or am i being too niave :)

Mr.Math
 4 years ago
Best ResponseYou've already chosen the best response.1You can deal with it as \(y'+y=x^3\).

Mr.Math
 4 years ago
Best ResponseYou've already chosen the best response.1I just integrated both sides, as you can see.

TuringTest
 4 years ago
Best ResponseYou've already chosen the best response.2thanks guys, makes sense :D (I was afk)

phi
 4 years ago
Best ResponseYou've already chosen the best response.3@ami wolfram says we can get to the same answer, by integrating the solution to your problem http://www.wolframalpha.com/input/?i=y%27%2By%3D+3x%5E2 http://www.wolframalpha.com/input/?i=y%27%27%2By%27%3D+3x%5E2 nice insight!
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