Concept explainers
Determine the intervals for which Theorem
a.
b.
(a)
The intervals for which Theorem
Answer to Problem 1RP
Solution:
Explanation of Solution
Given:
The given differential equation is
Approach:
Theorem
Suppose
So, here we will find the interval in which
Calculation:
Now
So,
Therefore
Conclusion:
Hence, the interval in which the theorem guarantees unique solution of the problem is
(b)
The intervals for which Theorem
Answer to Problem 1RP
Solution:
Explanation of Solution
Given:
The given differential equation is
Approach:
We will find the interval in which coefficient of given differential equation are continuous.
Calculation:
Simplifying the given differential equation
Here
So,
Therefore,
Conclusion:
Hence, the interval in which the theorem guarantees unique solution are
Want to see more full solutions like this?
Chapter 6 Solutions
Fundamentals of Differential Equations and Boundary Value Problems
- 3. Let X1, X2,..., X, be independent, Exp(1)-distributed random variables, and set V₁₁ = max Xk and W₁ = X₁+x+x+ Isk≤narrow_forward7. Consider the function (t)=(1+|t|)e, ER. (a) Prove that is a characteristic function. (b) Prove that the corresponding distribution is absolutely continuous. (c) Prove, departing from itself, that the distribution has finite mean and variance. (d) Prove, without computation, that the mean equals 0. (e) Compute the density.arrow_forwardSo let's see, the first one is the first one, and the second one is based on the first one!!arrow_forward
- 1. Show, by using characteristic, or moment generating functions, that if fx(x) = ½ex, -∞0 < x < ∞, then XY₁ - Y2, where Y₁ and Y2 are independent, exponentially distributed random variables.arrow_forward4. In each case, sketch the closure of the set: (a) -л 0.arrow_forwardFind the volume of the parallelepiped determined by the vectors a = (3, 5, −1), ☎ = (0, 3, 1), c = (2,4,1).arrow_forward
- 1. For each of the functions below, describe the domain of definition that is understood: 1 (a) f(z) = (b) f(z) = Arg z²+1 Z 1 (c) f(z) = (d) f(z) = 1 - | z | 2° Ans. (a) z±i; (b) Rez 0.arrow_forward1. Show, by using characteristic, or moment generating functions, that if 1 fx(x): x) = ½exarrow_forward1990) 02-02 50% mesob berceus +7 What's the probability of getting more than 1 head on 10 flips of a fair coin?arrow_forward
- Elements Of Modern AlgebraAlgebraISBN:9781285463230Author:Gilbert, Linda, JimmiePublisher:Cengage Learning,