(A) Determine the Solution of the Differential Equation $\frac { d y } { d x } = 2 y$

question 101

Essay

(a) Determine the solution of the differential equation $\frac { d y } { d x } = 2 y$ where $y ( 0 ) = 2$ .(b) Use the solution $y ( x )$ from part (a) to calculate $y ( 0.4 )$ .(c) Use Euler's Method with the given step sizes to estimate the value of $y ( 0.4 )$ for the equation given in part (a).(i) $h = 0.4$ (ii) $h = 0.2$ (iii) $h = 0.1$ (d) Sketch $y ( x )$ from part (b) and each of the Euler approximations from part (c) on the same coordinate plane.

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Definitions:

Negative Identity

A concept from Erikson's theory of psychosocial development, describing an identity formed by choosing values that are opposite of what is expected by significant others or society.

Thoughtful Consideration

entails careful and attentive deliberation or reflection before making a decision or forming an opinion.

Gender Role

Societal norms dictating the behaviors, attitudes, and activities deemed appropriate for men and women.

Parental Monitoring

Parents’ ongoing awareness of what their children are doing, where, and with whom.