Question

Solve the intitial value problem: dy/dx=x(6+x^2)^6, y(0)=0

Answer 1

just separate the variables and integrate

Answer 2

\[\frac{dy}{dx}=x(6+x^2)^6\]\[dy=x(6+x^2)^6dx\]\[\int dy=\int x(6+x^2)^6dx\]what do you get? (don't forget the integration constant for the indefinite integral)

Answer 3

...the integral involves a u-substitution

Answer 4

[(x^2+6)^7]/14

Answer 5

So...did I do that right?

Answer 6

yes good job
now use initial condition y(0) = 0 to solve for the constant
(x^2+6)^7 /14 + C = 0 .....x=0

Answer 7

Thank you. I got y=1/14(6+x^2)^7-(139968/7)
I feel confident with that

Answer 8

as you should :)