So I put the differential equation $y' = xy$ into Wolfram Alpha and it tells me the solution is $y(x) = c_1\,e^\frac{x^2}{2}$
- Can anybody explain to me how to sub this back into the original equation so as to verify it is the solution?
- And was the solution arrived at in the first place?
I really need to get a differntial equations book out of the library and go through it, which is what I plan to do at xmas when I have the time...but in the meantime I would appreciate if someone could explain this particular problem to me as it is starting to annoy me that I don't understand this stuff when doing numerical analysis (even though we can get by without knowing it).