Solve the Initial-Value Problem $y ^ { \prime \prime } + 2 y ^ { \prime } - 3 y = 0 , y ( 0 ) = 2 , y ^ { \prime } ( 0 ) = 1$

question 17

Multiple Choice

Solve the initial-value problem. $y ^ { \prime \prime } + 2 y ^ { \prime } - 3 y = 0 , y ( 0 ) = 2 , y ^ { \prime } ( 0 ) = 1$

• A) \(y = \frac { 1 } { 4 } e ^ { 2 x } + \frac { 7 } { 4 } e ^ { - 2 x }\)
• B) \(y = e ^ { x } + \frac { 1 } { 4 } e ^ { - 3 x }\)
• C) \(y = e ^ { 2 x } + \frac { 1 } { 4 } e ^ { - 2 x }\)
• D) \(y = \frac { 7 } { 4 } e ^ { x } + \frac { 1 } { 4 } e ^ { - 3 x }\)
• E) None of these

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Definitions:

Unfavorable Variances

Differences between actual and expected outcomes that negatively affect a business's financial performance.

Favorable Variances

Differences between actual and budgeted financial performance that result in a better-than-expected financial position.

Flexible Budget

A budget that adjusts or flexes with changes in volume or activity levels, providing a more useful tool for performance evaluation.

Variable Costs

Costs that vary directly with the level of production or business activity. Examples include raw materials, packaging, and direct labor.