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I am struggling so hard with Differential Equations.

This is my third time to take the class and I still feel like I am walking through the woods at midnight on an extremely dark night.

This is the problem that I am working on:

**dy/dx = x / (1 + y**

^{4})The instructions are to find (on paper) the general solution.

Well, I did that and got the following:

y + (y

^{5}/ 5) = (1/2) x

^{2}+ C

_{1}

Now, I am supposed to verify that the equation found is a solution to the differential equation.

Now, I know that the original equation can also be written as:

y' = x / (1 + y

^{4})

And, I know that I should be able to take the derivative of the general solution, then plug in and solve.

But, I also think (whoa... this is where it gets sketchy), that the general solution should be have the terms of y on the LHS and collected.

So, what did I miss this time? Substitution by parts? Some trig identity?

Please help me. I so wish that I got this.

I am ready to go dig ditches somewhere if this fog doesn't lift for me.

TIA