Differential Equations final

With Kushal

Differential Equations final

Chapter 2

Chapter 3

Chapter 4

Chapter 7

Chapter 2

Separable equations

Definition

Method for solving

Examples

Linear Equations

Definition

Method

Chapter 2

1. Separable
2. Linear
3. Exact

Chapter 3

1. Compartmental
2. Heating and cooling

Chapter 4

1. Homogeneous linear DE with real roots and complex roots
2. Non-homogeneous linear DE with

1. undetermined coefficients
2. variation of parameter

Chapter 7

1. Laplace transform with initial value

Chapter 2

Separable equations

Definition

A first order equation is separable if it can be written in the form of

Method for solving

1. Set the equation to the form as shown above.
2. Multiply by dx and by h(y) := 1/p(y) to obtain

3. Then integrate both sides:

4. Thus, we get H(y) = G(x) + C

Examples

Linear Equations

Definition

A linear first order equation can be expressed as

Note that:

1. the exponent of y is zero or one in all the terms
2. there are only an ordinary first order derivative

Method

1. Write down the equation in the standard form as follows

2. Calculate the integrating factor μ(x) by the formula

3. not to be continued. Lamar has great resources on differential equations at http://tutorial.math.lamar.edu/Classes/DE/Linear.aspx