Answer:

General Formulas and Concepts:
Pre-Algebra
Order of Operations: BPEMDAS
- Brackets
- Parenthesis
- Exponents
- Multiplication
- Division
- Addition
- Subtraction
Equality Properties
- Multiplication Property of Equality
- Division Property of Equality
- Addition Property of Equality
- Subtraction Property of Equality
Algebra I
- |Absolute Value|
- Functions
- Function Notation
- Exponential Rule [Multiplying]:

Algebra II
- Logarithms and Natural Logs
- Euler's number e
Calculus
Derivatives
Derivative Notation
Derivative of a constant is 0
Differential Equations
Antiderivatives - Integrals
Integration Constant C
Integration Property [Multiplied Constant]:

U-Substitution
Logarithmic Integration
Explanation:
Step 1: Define
Identify


Step 2: Rewrite
Separation of Variables
- Rewrite Derivative Notation:

- [Division Property of Equality] Isolate y's:

- [Multiplication Property of Equality] Rewrite Derivative Notation:

Step 3: Find General Solution Pt. 1
Integration
- [Equality Property] Integrate both sides:

- [1st Integral] Integrate [Logarithmic Integration]:

Step 4: Identify Variables
Identify variables for u-substitution for 2nd integral.
u = 2 + x²
du = 2xdx
Step 5: Find General Solution Pt. 2
- [2nd Integral] Rewrite [Integration Property - Multiplied Constant]:

- [2nd Integral] U-Substitution:

- [2nd Integral] Integrate [Logarithmic Integration]:

- [Equality Property] e both sides:

- Simplify:

- Rewrite [Exponential Rule - Multiplying]:

- Simplify:

- Back-Substitute:

Our general solution is
.
Step 6: Find Particular Solution
- Substitute in point:

- Evaluate |Absolute Value|:

- |Absolute Value| Evaluate exponents:

- |Absolute Value| Add:

- |Absolute Value| Evaluate:

- [Division Property of Equality] Isolate C:

- Rewrite:

- Substitute in C [General Solution]:

∴ Our particular solution is
.
Topic: AP Calculus AB/BC (Calculus I/II)
Unit: Differential Equations
Book: College Calculus 10e