Solve the Differential Equation $$\frac { d y } { d x } = 7 x ^ { 6 } e ^ { - y }$$

question 1

Multiple Choice

Solve the differential equation.
- $$\frac { d y } { d x } = 7 x ^ { 6 } e ^ { - y }$$

• A) \(y = \ln \left( 7 x ^ { 7 } + C \right)\)
• B) \(y = x ^ { 7 } + C\)
• C) \(y = C \ln \left( x ^ { 7 } \right)\)
• D) \(y = \ln \left( x ^ { 7 } + C \right)\)

---

Definitions:

Psychoanalysis

A set of theories and therapeutic techniques related to the study of the unconscious mind, developed by Sigmund Freud, which seeks to treat mental disorders.

Theoretical Background

The collection of concepts, models, and theories that form the foundation and framework for understanding a particular area of study or research.

Key Concepts

Foundational or core ideas that are essential for understanding a particular field or subject matter.

Electroconvulsive Therapy

A therapy often applied to major depressive disorders that involves the use of electrical currents to generate short seizures in the brain.