Question

differential equations solve
(1+2x2)y’=x√(1+2x2)+8xy
x2 is square of x

Answer 1

I believe this can be solved with an integrating factor

Answer 2

play around with it for a sec and you get:

y'- (8x/1+2x2) y = x/sqrt(1+2x2)

Answer 3

which is the standard form for the integrating factor technique

Answer 4

http://en.wikipedia.org/wiki/Integrating_factor

Answer 5

wow they make that so confusing haha

Answer 6

basically your integrating fator is e^intP(x) dx

Answer 7

you multiply that through your equation

Answer 8

you take the integral of both sides

Answer 9

the left side just becomes your integrating factor times y

Answer 10

the right side you have to take an integral

Answer 11

solve for y and you end up with a general solution in terms of x and a constant

Answer 12

http://www.sosmath.com/diffeq/first/lineareq/lineareq.html