Maclaurin series

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Homework Statement



for this question, i found that my coefficient of x^4 is wrong... after applying the maclaurin series formula, i would get the coefficient of X^4 is -5/96.... but the exact ans is -1/96... can anyone check which part is wrong?

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The Attempt at a Solution

 

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  • #2
Dick
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Homework Statement



for this question, i found that my coefficient of x^4 is wrong... after applying the maclaurin series formula, i would get the coefficient of X^4 is -5/96.... but the exact ans is -1/96... can anyone check which part is wrong?

Homework Equations





The Attempt at a Solution


For one thing y''(0)=(-1/2) not (+1/2). Can you check how you got that? I think you made an algebra mistake. Then can you spell out how you got y'''(0) and y''''(0) a little more clearly?
 
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  • #3
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For one thing y''(0)=(-1/2) not (+1/2). Can you check how you got that? I think you made an algebra mistake. Then can you spell out how you got y'''(0) and y''''(0) a little more clearly?

this is actually the question from my book(gt it from my senior), do u mean the proving part, the third term is -1/2 y^2 ?? for y'''(0) and y''''(0) , i differentiate the equation y(d2y/dx2) + (dy/dx)^2 + 1/2y^2 a few times to get y''' and y'''' .... refer to the photo attached...
 

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  • #4
Dick
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this is actually the question from my book(gt it from my senior), do u mean the proving part, the third term is -1/2 y^2 ?? for y'''(0) and y''''(0) , i differentiate the equation y(d2y/dx2) + (dy/dx)^2 + 1/2y^2 a few times to get y''' and y'''' .... refer to the photo attached...

The photo you attached seems to be from a different problem and what you have in the original statement is pretty hard to read. I think if you do it again more carefully you should get the correct answer.
 
  • #5
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can you check my working again? i checked it many times but i just cant dont know where's my mistake
 
  • #6
Dick
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can you check my working again? i checked it many times but i just cant dont know where's my mistake

I told you a long time ago. y''(0) should be -1/2, not +1/2. Didn't you check that?
 

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