Question

Find the solution in the form y=f(x) for the differential equation:
dy/dx= 2xy
Help is greatly appreciated!

Answer 1

so first I figure I should separate and integrate:
dy/y= 2x dx
Int. dy 1/y= Int. 2x dx

Answer 2

I got: ln(y) +C = x^2 +C2
which is ln(y)= x^2 +C
I'm not entirely sure how to get rid of the ln...

Answer 3

you can make each side the exponent of e
\[ e^{\ln(y)} = e^{x^2+C} \]

Answer 4

people rewrite the right side as
\[ e^{x^2} e^C = B e^{x^2} \]
where B represents the arbitrary constant e^C

Answer 5

e^ln(y) simplifies to y

Answer 6

so y= e^(x^2+C) but I could rewrite as y= ke^(x^2) (using 'k' as your "B")

Answer 7

yes

Answer 8

thank you very much for your help! I understand this now, the problem was that it is multiple choice and the answers didn't match up. but I see that I can write y= e^(x^2 +C) as y= ke^(x^2) so it works out!