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

question 55

Multiple Choice

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

• A) \(y = C x e ^ { 2 x }\)
• B) \(y = C e ^ { - 2 / x }\)
• C) \(y = e ^ { 1 / x } x + C e ^ { 1 / x }\)
• D) \(y = x ^ { 2 } e ^ { - 1 / x } + C e ^ { - 1 / x }\)
• E) none of these

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Definitions:

Discount on Bonds Payable

The difference between the par (or face) value of a bond and its lower issuing price, representing an additional cost of borrowing for the issuer.

Straight-Line Amortization

A method of evenly spreading the cost of an intangible asset over its useful life.

Discount at Issuance

The difference between the face value of a bond and its selling price when the bond is sold for less than its face value.

Effective Rate of Interest

The actual cost of borrowing or the actual return on savings, taking into account the effect of compounding interest.