Correcting Maclaurin Series Coefficient of x^4 | Homework Help

[delsoo]

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

 

[Dick]

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?

 

[delsoo]

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...

 

[Dick]

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.

 

[delsoo]

can you check my working again? i checked it many times but i just can't don't know where's my mistake

 

[Dick]

can you check my working again? i checked it many times but i just can't don't 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?