Not what you're looking for?
Please see the attached file for the fully formatted problems.
(i) Consider the differential equation:
x. = x^2 , x(0) given x(0)>0
Find the solution of x(t) of this equation in terms of x(0) and show that there is a T, which depends on x(0), such that lim x(t) = infinity t --> T-
(ii) Find the solution of the differential equation
x.. - x = e^-t/2 , x(0) = 0, (0) = 1,
Using the reduction of order method.
Purchase this Solution
Two differential equations are solved. The differential equations for reduction of order methods are determined. Limits that go to infinity are given.
Solution. (1) From x'=x^2, we have
Integrate both sides to get
where C is a constant. According to the initial condition we know that, when t=0, x=x(0)>0. So C=-1/x(0). The ...
- BSc , Wuhan Univ. China
- MA, Shandong Univ.
- "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!"
Purchase this Solution
Free BrainMass Quizzes
In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.
Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.
Some questions on probability
This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.
Understanding of how geometry applies to in real-world contexts