Mathematics

Question 1

What are the 6 steps to solving a first order linear differential equation for a general solution?

What would you do for a particular solution?

Answer 1

1) Get in form dy/dx + P(x)y = Q(x)
2) Determine the IF (Integrating Factor)
3) Multiply both sides of equation by IF
4) Reverse the product rule
( Form u’v + uv’ back to d/dx (uv) )
5) Integrate both sides
6) Rearrange/simplify for a general solution

For a particular solution, substitute in initial conditions to get a value for integration constant and any other arbitrary constants.

Question 2

What is the integrating factor? (IF)

Answer 2

IF = e^∫P(x)dx