Solve the Differential Equation $$\frac { d y } { d x } = 3 x ^ { 2 } e ^ { - y }$$

question 122

Multiple Choice

Solve the differential equation.
- $$\frac { d y } { d x } = 3 x ^ { 2 } e ^ { - y }$$

• A) \(y = \ln \left( x ^ { 3 } + C \right)\)
• B) \(y = \ln \left( 3 x ^ { 3 } + C \right)\)
• C) \(y = C \ln \left( x ^ { 3 } \right)\)
• D) \(y = x ^ { 3 } + C\)

---

Definitions:

Injection Mold

A manufacturing process for producing parts by injecting material into a mold.

Drill Press

A machine tool used for drilling holes in various materials, where the drill is pressed into the workpiece by a motor-driven or manual lever.

Value-based Pricing

A pricing strategy where the price is set based on the perceived value of the product or service to the customer rather than on the cost of the product or market prices.

Preventive Maintenance

Regular and routine maintenance performed on equipment and machinery to prevent unexpected failures and downtime.