Originally Posted by

**bigroo** Hello all,

Can you see if this makes sense please.

$\displaystyle \frac{dy}{dx} = \frac{e^{-4x} - x}{e^{-4x} + 2x^{2} + 1} when y(0)=4$

$\displaystyle \int \frac{f'(x)}{f(x)}=ln(f(x))+c$

$\displaystyle -\frac{1}{4} \int \frac{4e^{-4x} + 4x}{e^{-4x} + 2x^{2} +1} dx$

$\displaystyle y=\frac{1}{4} ln (e^{-4x} + 2x^{2} +1) + c$

$\displaystyle y(0)=4$

$\displaystyle 4=(1)C=4$

$\displaystyle y=\frac{1}{4} ln (e^{-4x} + 2x^{2} + 1) + 4$

I'm not sure but I think it all goes wrong when I put all equal to y.

Would appreciate any help please.

Thanks in advance.