Solve the Initial Value Problem Using an Integrating Factor $y ^ { \prime }$

question 58

Multiple Choice

Solve the initial value problem using an integrating factor.
-t $y ^ { \prime }$ + 3y = 5t; $y ( 1 ) = 1$ , t > 0

• A) y = \(\frac { 5 } { 4 }\) t - \(\frac { 1 } { 4 t ^ { 3 } }\)
• B) y = \(\sqrt { \frac { 4 } { 3 } t ^ { 2 } }\) + 1 - \(\sqrt { \frac { 4 } { 3 } }\)
• C) y = 5 \(t ^ { 2 }\) - 4t
• D) y = 5 \(t ^ { 3 }\) - 4 \(t ^ { 2 }\)

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Definitions:

Optimal Pollution Control

The regulation of pollution to maximize social welfare by balancing the costs of pollution control against the benefits of reducing pollution.

Economists

Professionals who study how societies use scarce resources to produce valuable goods and services and distribute them among different people.

Positive Externalities

Benefits that are enjoyed by a third-party or the society at large as a result of an economic transaction, but these benefits are not reflected in the market price.

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The economic issue of having limited resources to satisfy unlimited wants and needs, necessitating choices and priorities in allocation.