Use Euler's Method with Step Size $0.25$ To Estimate $y ( 1 )$

question 39

Multiple Choice

Use Euler's method with step size $0.25$ to estimate $y ( 1 )$ , where $y ( x )$ is the solution of the initial-value problem. Round your answer to four decimal places.
$$y ^ { t } = 4 x + y ^ { 2 } , y ( 0 ) = 0$$

• A) \(y ( 1 ) = 4.1622\)
• B) \(y ( 1 ) = 1.6622\)
• C) \(y ( 1 ) = 3.1622\)
• D) \(y ( 1 ) = 3.1622\).
• E) \(y ( 1 ) = 2.6622\).

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Definitions:

Self-actualization

A concept in psychology representing the realization or fulfillment of one's talents and potentialities, especially considered as a drive or need present in everyone.

Needs-hierarchy Theory

A psychological theory proposed by Abraham Maslow that categorizes human needs into a hierarchical structure, from basic physiological needs to self-actualization.

Maslow

Abraham Maslow was an American psychologist best known for creating Maslow's hierarchy of needs, a theory of psychological health predicated on fulfilling innate human needs in priority, culminating in self-actualization.

Maslow

Refers to Abraham Maslow, an American psychologist who developed the hierarchy of needs theory, emphasizing the importance of self-actualization.