The Problem $y ^ { \prime \prime } + x y y ^ { \prime } = 0 , y ( 0 ) = 0 , y ^ { \prime } ( 0 ) = 1$

question 30

Multiple Choice

The problem $y ^ { \prime \prime } + x y y ^ { \prime } = 0 , y ( 0 ) = 0 , y ^ { \prime } ( 0 ) = 1$ can be written as a system of two equations as follows.

• A) \(y ^ { \prime } = u , u ^ { \prime } = x y u , y ( 0 ) = 0 , u ( 0 ) = 0\)
• B) \(y ^ { \prime } = u , u ^ { \prime } = - x y u , y ( 0 ) = 1 , u ( 0 ) = 0\)
• C) \(y ^ { \prime } = u , u ^ { \prime } = x y u , y ( 0 ) = 1 , u ( 0 ) = 0\)
• D) \(y ^ { \prime } = u , u ^ { \prime } = x y u , y ( 0 ) = 0 , u ( 0 ) = 1\)
• E) \(y ^ { \prime } = u , u ^ { \prime } = - x y u , y ( 0 ) = 0 , u ( 0 ) = 1\)

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Definitions:

Bailor's Sole Benefit

Refers to a situation in a bailment where the benefit of the arrangement is exclusively for the bailor, with the bailee undertaking the responsibility without receiving any benefit.

Without Compensation

Performing an action or providing a service without receiving any form of payment or benefit in return.

Heir

A person legally entitled to receive a share of the deceased's estate.

Decedent

A person who has died, especially in context relating to the disposal of their estate.