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Determine If the Given Function Y = F(x) Is a Solution

question 109

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Determine if the given function y = f(x) is a solution of the accompanying differential equation.
- y=13x13xettdtx2y+xy=13e3x\begin{array} { l } y = \frac { 1 } { 3 x } \int _ { 1 } ^ { 3 x } \frac { e ^ { t } } { t } d t \\x ^ { 2 } y ^ { \prime } + x y = \frac { 1 } { 3 } e ^ { 3 x }\end{array}

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Definitions:

FICA-Medicare

A federal payroll (or employment) tax contribution towards Medicare, part of the FICA taxes in the United States.

Cumulative Earnings

The total amount of net income (or loss) earned by a company over a period of time, often used to measure its financial performance.

OASDI

An acronym for Old-Age, Survivors, and Disability Insurance, which is a comprehensive federal benefits program that provides benefits to eligible American workers and their families.

Medicare

A federal health insurance program in the United States primarily for people aged 65 and over, as well as for some younger people with disabilities.

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