Consider the Differential Equation $\frac { d y } { d t } = y - t$

question 16

Essay

Consider the differential equation $\frac { d y } { d t } = y - t$ .(a) What are the equilibrium solutions?
(b) What are the points in the $t y$ -plane at which the slope of the solution curve is $0$ ?
(c) What are the points in the $t y$ -plane at which the slope of the solution curve is $1$ ?
(d) What are the points in the $t y$ -plane at which the slope of the solution curve is -1?
(e) Use the information from above to sketch the direction field for the given differential equation.

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Definitions:

Delayed-response Task

A test used in research to assess memory and cognitive function, requiring subjects to remember information after a time delay.

NMDA Receptors

A type of glutamate receptor in the brain that plays a key role in synaptic plasticity, memory, and learning.

AMPA Receptors

AMPA receptors are a type of glutamate receptor that mediates fast synaptic transmission in the brain, playing critical roles in brain function and plasticity.

Glutamate

An amino acid that acts as a key neurotransmitter in the brain, involved in learning, memory, and the regulation of the nervous system.