Solve the Differential Equation $$x ^ { 2 } \frac { d y } { d x } - y = 2 x ^ { 3 } e ^ { - 1 / x }$$

question 33

Short Answer

Solve the differential equation.
$$x ^ { 2 } \frac { d y } { d x } - y = 2 x ^ { 3 } e ^ { - 1 / x }$$

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Definitions:

Organic Compound

A chemical compound containing carbon atoms bonded to hydrogen atoms in a structure.

Cyclopentanecarboxylic Acid

An organic compound characterized by a five-membered ring structure bonded to a carboxylic acid group, often involved in the synthesis of pharmaceuticals and fine chemicals.

Thionyl Chloride

A reactive chemical compound used for converting alcohols into chlorides and as a reagent in various organic synthesis reactions.

Organic Product

A chemical compound or substance that is based on carbon skeletons and is produced by living organisms.