Question

I need help with separable equations

Answer 1

\[dy/dx = 72/3x^5y(1+3x^6)^{1/3}\]

Answer 2

\[dy/dx = (72/3)x^5y(1+3x^6)^{1/3}\]

Answer 3

\[\frac{dy}{dx} = \frac{72}{3x^5y(1+3x^6)^{1/3}}\]?

Answer 4

please use lots of steps

Answer 5

I'm not really sure how you got to this part.. How and why would you put the whole equation on the bottom

Answer 6

\[\frac{dy}{dx} = \frac{72}{3}x^5y(1+3x^6)^{1/3}\]
Is it like this?

Answer 7

\[\frac{1}{y}dy = 24x^5(1+3x^6)^{1/3}dx\]

Answer 8

ok ive gotten that far.

Answer 9

however this is where things get fuzzy. I know I need to take the integral of both sides but I'm just not getting the answer I should be

Answer 10

\[\int\frac{1}{y}dy=\int\left(24x^5(1+3x^6)^{1/3}\right)dx\]

Answer 11

\[\ln{y}=\int\left(24x^5(1+3x^6)^{1/3}\right)dx\]

Answer 12

\[\ln{y}=\int\left(24x^5(1+3x^2)\right)dx\]

Answer 13

\[\ln{y}=\frac{24}{6}x^6 + \frac{72}{8}x^8 +C\]

Answer 14

\[\ln{y}=4x^6+9x^8+C\]

Answer 15

\[y=e^{x^6(4+9x^2)}+A\]