Diff EQ, can't see what I did wrong expressing this seperable

[mr_coffee]

Hello everyone. I don't see how this problem is wrong, i never do.
Here it is:
Solve the differential equation
(y^{15} x ){dy}/{dx} = 1 + x.
Use the initial condition y(1) = 3.
Express y^{16} in terms of x.
y^{16} = ?

y^15*dy = (1+x)/x dx;

I integrated both sides and got:
(y^16)/16 = ln(x)+x+c;
y^16 = 16(ln(x)+x+c);
3^16 = 16 + c
C = 43046705

I submitted this:
y^{16} = 16*(ln(x)+x+43046705)

which was inccoret, any ideas? thank u!

 

[benorin]

Try y^{16} = 16*ln(x)+16*x+43046705

also, you may need to put ln(|x|) instead of ln(x).

 

[mr_coffee]

Nicely done benorin that was correct! i done f'ed up! thank you again!