A Function Y (X) Satisfies the Differential Equation $\frac { d y } { d x } = y ^ { 2 } - 4 y + 3$

question 141

Essay

A function y (x) satisfies the differential equation $\frac { d y } { d x } = y ^ { 2 } - 4 y + 3$ .(a) What are the constant solutions of the equation?
(b) For what values of $y$ is $y$ increasing?
(c) The equation shows that $\frac { d y } { d x }$ is independent of $x$ . Using this observation, what can you say about the relationship of the graphs of the non-constant solutions of the equation?

Recognize appropriate blocking variables in experimental designs.

Understand the concept of a time series and identify its four components: long-term trend, cyclical variation, seasonal variation, and random variation.

Apply exponential smoothing techniques to forecast future values of a time series.

Identify the effects of different smoothing constants on time series forecasts and the speed of reaction to changes in data trends.

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