Review of 11.1-3 and 11.4 (Separation of Variables)

Question 1

What is the separation of variables?

Answer 1

a method to solve differential equations by separating terms involving x and y on opposite sides of the equation.

Question 1

What kind of differential equations can be solved by the separation of variables?

Answer 1

This method is used for first-order differential equations that can be written in the form:
dy/dx=g(x)h(y)

Question 2

What is the steps of the separation of variables?

Answer 2

1. The goal is to rewrite the equation so all y-terms are on one side with dy and x-terms are on the other side with dx

2.allowing us to integrate both sides separately.

3.isolate for y

Question 3

What is included in the general solution in the separation of variables and why?

Answer 3

The general solution includes an arbitrary constant C after integrating, representing a family of solutions to the differential equation.

Question 4

how do you find the particular solution?

Answer 4

A particular solution is found by using an initial condition to solve for C in the general solution.

Question 5

What is the result of integrating both sides in the example
1/𝑦 𝑑𝑦=𝑥𝑑𝑥

Answer 5

ln∣y∣= x^(2)/2+C