Problem 5 Draw a direction field for the given differential equation. Based on the direction field, determined the behavior of y as t→ o, If this behavior depends on the initial value of y at t = 0, describe the dependency. y' = 3+ 2y
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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HW1 for Ch1.1, Differential Equations
Problem 5
Draw a direction field for the given differential equation. Based on the direction field,
determined the behavior of y as t- 0o. If this behavior depends on the initial value of y at
t = 0, describe the dependency.
y' = 3+ 2y
Problem 21
Draw a direction field for the given differential equation. Based on the direction field,
determine the bchavior of y as t → 0o. If this behavior depends on the initial value of y at
t = 0, describe the dependency. Note that the right-hand sides of these equations depend on t
as well as y; therefore, their solutions can exhibit more complicated behavior than the above
problem.
y' = -3 +t-y
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HW2 for Ch2.1, Differential Equations
Problem 10 & 12
Find the solution of the given initial value problems.
y' + 3y = te-3,
y(1) = 0
ty' + 2y = 2 sint,
y) = 1,
t>0
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