Solve the Initial Value Problem for X as a Function $$( t + 4 ) \frac { d x } { d t } = x ^ { 2 } + 1 , \quad t > - 4 , x ( 1 ) = \tan 1$$

question 220

Multiple Choice

Solve the initial value problem for x as a function of t.
- $$( t + 4 ) \frac { d x } { d t } = x ^ { 2 } + 1 , \quad t > - 4 , x ( 1 ) = \tan 1$$

• A) \(x = \tan [ \ln | t + 4 | - \ln 5 ]\)
• B) \(x = \tan [ \ln | t + 4 | - \ln 5 + 1 ]\)
• C) \(x = \tan ^ { - 1 } [ \ln | t + 4 | - \ln 5 + 1 ]\)
• D) \(x = \frac { 1 } { t + 4 } - \frac { 1 } { t - 5 }\)

---

Definitions:

Cognitive Therapy

A form of psychotherapy that aims to modify dysfunctional emotions, behaviors, and thoughts through a process of identifying and challenging negative patterns and beliefs.

Psychoanalysis

A therapeutic approach created by Sigmund Freud that explores unconscious motivations and conflicts as they relate to mental disorders.

Catharsis

The process of releasing, and thereby providing relief from, strong or repressed emotions, often through art, writing, or speaking.

Therapeutic Intervention

Professional actions undertaken to help individuals with physical, emotional, cognitive, or social issues achieve optimum functioning and wellness.