Question

While using the method of variation of parameters how to we get the equation set
u1'y1 + u2'y2 = 0
u1'y1' + u2'y2' = g(x)
after subsituting the assumed solution into the equation.

where g(x) is the forcing funtion of the the original second degree linear diff eq.

Answer 1

http://tutorial.math.lamar.edu/Classes/DE/VariationofParameters.aspx

Answer 2

yes, i read that however ,it list (3) or eq1 as an assumption .This implies the the solution set we get from using this method is a subspace of the true solution space.

Answer 3

if no it begs the question hoe can we be sure that the the basis produced by this method with this assumption spans the solution space i.e. encompasses all possible solutions.

Answer 4

sorry *if not

Answer 5

I guess what you really want to know is why this assumption is produced like some sort of magic trick, rabbit out of a hat.

No idea, I'll see if I can find out.

Answer 6

precisely, and thank you in advance.