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Differential equations

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I need to know how to find a particular solutions to an initial conditions. i know how to find the explicit solution of a differential equation but cannot remember how to find particular solutions. please show your working to help me understand. thanks

Problems (also attached):

Given the attached information:

1) So how do I find the corresponding particular solution that satisfies the initial condition y = 1 when x = 0. ?

2) What is the value of y given by this particular solution when x = 7? Give your answer to two decimal places. (Note that your calculator should be in radian mode for this calculation) why??

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This solution is comprised of a detailed explanation to answer how do I find the corresponding particular solution that satisfies the initial condition y = 1 when x = 0 and what is the value of y given by this particular solution when x = 7.

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see attachment.

Differential equations

From the differential equation,

I know that the general solution is,

And in implicit form is,

Therefore the corresponding explicit form of the general solution is,

1) So how do I find the corresponding particular solution that satisfies the initial condition y = 1 when x = 0. ?

If we know the general ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "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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