Find the Solution of the Differential Equation $\frac { d y } { d t } = 3 t ^ { 2 } - \frac { 4 } { \sqrt { t } }$

question 5

Multiple Choice

Find the solution of the differential equation $\frac { d y } { d t } = 3 t ^ { 2 } - \frac { 4 } { \sqrt { t } }$
with initial condition, $y ( 0 ) = 4$ .

• A) \(t ^ { 3 } - 2 \sqrt { t } + 4\)
• B) \(t ^ { 3 } - 8 \sqrt { t } + 4\)
• C) \(t ^ { 3 } + 2 t ^ { \frac { 3 } { 2 } } + 4\)
• D) \(t ^ { 3 } - 2 t \sqrt { t } + 4\)
• E) \(t ^ { 3 } + 4 \sqrt { t } + 4\)

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Definitions:

Schizophrenia

A severe mental disorder characterized by distortions in thinking, perception, emotions, language, sense of self, and behavior, greatly affecting how a person relates to reality.

Normal Functions

Refers to the typical and expected processes or operations of systems, whether biological, mechanical, or psychological.

Negative Symptoms

Symptoms commonly associated with schizophrenia or other mental disorders, characterized by a lack or reduction of normal functions, such as blunted emotions or social withdrawal.

Schizophrenia

A chronic psychological condition characterized by a disruption in the connection among cognition, affect, and conduct, resulting in incorrect perceptions, improper behaviors and emotions, retreat from actuality and social connections into make-believe and false beliefs, along with a feeling of psychological disintegration.