Solve the Differential Equation $$y ^ { t } = x ^ { 2 } e ^ { - \sin x } - y \cos x$$

question 17

Multiple Choice

Solve the differential equation. Select the correct answer.
$$y ^ { t } = x ^ { 2 } e ^ { - \sin x } - y \cos x$$

• A) \(y = 2 \mathrm { Ce } e ^ { - \sin x }\)
• B) \(y = e ^ { - \sin x } + 2 C x ^ { 2 }\)
• C)
• \(y = \frac { 1 } { 3 } x + C e ^ { - \cos x }\)
• D) \(y = \left( 3 x ^ { 3 } + C \right) e ^ { - x } \sin x\)
• E)
• \(y = \left( \frac { 1 } { 3 } x ^ { 3 } + C \right) e ^ { - \sin x }\)

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Definitions:

Erythropoiesis

The production of red blood cells (erythrocytes) in the bone marrow, a process regulated by the hormone erythropoietin.

Macrophages

Large white blood cells that are part of the immune system, engulfing and digesting cellular debris, foreign substances, microbes, and cancer cells.

Lymphocytes

A kind of leukocyte that plays a role in the immune system, aiding in the defense of the body from infectious diseases and external threats.

Neutrophils

A type of white blood cell that is part of the immune system, involved in protecting the body against infections by ingesting microorganisms and releasing enzymes.