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Find the particular solution of the differential equation 4d²y/dx² -4dy/dx + y = 0 y(0)=0, y´(0)=1.

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Please find the particular solution of the differential equation below satisfying the given initial conditions.

The equation needs to be put in standard form (s² + bs + c = 0). The roots need to be found, and then plugged into the appropriate general formula that satisfies whether b² + 4c is less than, greater than, or equal to zero. After finding the general solution, solve for the values of C given the initial conditions. Then rewrite the equation with those values.
Please show all details in the solution. Thank you

4d²y/dx² -4dy/dx + y = 0 y(0)=0, y´(0)=1

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Find the particular solution of the differential equation
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Please find the particular solution of the differential equation below satisfying the given initial conditions.
The ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
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  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
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