1. ## dy/dx = 12yx^3

The question is:
dy/dx = 12yx^3, y(0) = 6

My work:
(My work is attached) but here is the final answer I get y = 5e^(3x^4) which is supposedly wrong.

Any help would be greatly appreciated!

2. Originally Posted by s3a
The question is:
dy/dx = 12yx^3, y(0) = 6

My work:
(My work is attached) but here is the final answer I get y = 5e^(3x^4) which is supposedly wrong.

Any help would be greatly appreciated!
Separate the variables

$\frac{dy}{y} = 12x^3\,dx$

$\ln |y| = 3x^4 + C$

$|y| = e^{3x^4+C} = Ae^{3x^4} \text{ where } A = e^C$

Initial condition: (0,6)

$6 = Ae^0 \: \rightarrow \: A = 6$

Therefore the equation is $|y| = 6e^{3x^4}$