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

question 7

True/False

Determine if the given function y = f(x) is a solution of the accompanying differential equation.
-Differential equation: $y ^ { \prime } = e ^ { - 7 x } - 7 y$
Initial condition: $y ( 0 ) = 0$
Solution candidate: $y = 7 xe ^ { - 7 x }$

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Definitions:

Budgets

Detailed plans that outline expected income and expenditures over a specific period, often used by individuals, organizations, or governments to manage finances.

Marginal Rate

The rate at which one quantity changes relative to a change in another quantity.

Substitution

The economic principle where consumers replace pricier items with less expensive alternatives when prices rise or their purchasing power decreases.

Indifference Curve

This is a graph representing different bundles of goods between which a consumer is indifferent, meaning that each combination offers the same level of utility to the consumer.