# Solving a differential equation with only one variable

So for some reason I'm blanking on solving a seemingly easy question:

$(8x + \cos(x))\mathrm dx + (4x^2 + 7\sin(x) + 1)\mathrm dy = 0$

Which I'm currently assuming is going to be solved using an integrating factor since as far as I can tell it isn't exact, linear, or homogenous (and I would need variables to separate for it to be separable).

Edit: there was a typo in the question, please ignore.

## 1 Answer

Write $$\frac{dy}{dx}=-\frac{8\,x + \cos x}{4\,x^2 + 7\sin x + 1}.$$ Since there is no $y$ on the right hand side, all you have to do is to integrate with respect to $x$. However, the integral cannot be represented in terms of elementary functions. Are you sure there is not a $7$ in front of $\cos x$? (in which case the numerator would be the derivative of the denominator.)

• Just heard back from my professor and there was indeed supposed to be a 7 in front of the cos, so I guess my confusion was pretty appropriate. Thanks. – A.Caines May 20 '16 at 16:54