Where have I gone wrong in trying to solve this ODE? I'm trying to solve: $\frac{dy}{dx}=\frac{x+y-1}{x+4y+2}$.
Attached is a picture of my working.
Could someone please  tell me where I'm going wrong?

I'm tried both Maple and Wolfram and neither of them gives me a 'nice' answer.
I know it's wrong as I've implicitly differentiated my answer and I get the wrong algebraic value of $\frac{dy}{dx}$. Thanks.

To continue on from my comment (and losing the absolute value signs for the moment, since we are taking fourth roots - but note the fourth roots vanish in the calculation) your complicated expression can have fractions cleared to give:
$$(x-2y-4)^{\frac 34}(x+2y)^{\frac 14}=\frac 1C$$
Implicit differentiation then gives
$$\frac 34(1-2\frac{dy}{dx})(x-2y-4)^{-\frac 14}(x+2y)^{\frac 14}+\frac 14(1+2\frac{dy}{dx})(x-2y-4)^{\frac 34}(x+2y)^{-\frac 34}=0$$ Which simplifies nicely to $$3(1-2\frac{dy}{dx})(x+2y)=-(1+2\frac{dy}{dx})(x-2y-4)$$ and gathering the terms together then gives:$$3x+6y+x-2y-4=(6x+12y-2x+4y+8)\frac {dy}{dx}$$ whence $$\frac {dy}{dx}=\frac{x+y-1}{x+4y+2}$$
as required (apart from being careless about signs).
