Hi everyone. I'm stuck with this problem on particular antiderivatives:

"The points (1,3) and (0,2) are on a curve, and at any point (x,y) on the curve, d

^{2}y/dx

^{2 }= 2 - 4x. Find an equation for the curve."

I was able to get dy/dx from solving, and I got 2x - 2x

^{2} + C. Now I'm unsure what to do... I did, however, try and guess my way through the problem (oops). I eventually came up with the final answer of y = x

^{2} - 2x

^{3}/3 - 2x + 14/3. If it happens to actually be the answer, please tell me.

Can someone please lead me in the right direction? Thank you so much!

NOTE: Attached is my solution to the problem just in case you would like to see how I got my (guessed) final answer.