The slope field for a differential equation is shown in the figure. Determine the general solution of this equation

Question

anonymous · Answer

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anonymous · Answer

answer choices 

 y=Cx^2
 x=Cy^2
 x^2 – y^2 = C^2
 x2 + y2 = C^2

anonymous · Answer

okay so i know i have to reverse engineer this but i'm not doing too well

ganeshie8 · Answer

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anonymous · Answer

so i should just isolate the variables of each of the answer choices and derive each side right and graph all the diff equations i get and match it to the one im given , is that right?

astrophysics · Answer

Could you not let x = 1 and y = 1 and then set it up as dy/dx that way you can see the slope easier?

ganeshie8 · Answer

To my knowledge that slope field corresponds to a differential equation : 
$$y'=2x$$

the family of solutions must look something like
$$y = x^2+C$$

anonymous · Answer

http://www.mathscoop.com/calculus/differential-equations/slope-field-generator.php this might help

anonymous · Answer

and yes you are correct @ganeshie8 i just cant get the differential equation when onlly given the solution to a differential equation

anonymous · Answer

okay can you walk me through your answer ?

astrophysics · Answer

Wait, I don't know if it's right, but what I was thinking is as I said above, let x = 1, y = 1 or what ever and just let dy/dx = x/y^2 and then plug in the values and just observe the points...not sure if that's a good method haha, ganeshie definitely knows more.

ganeshie8 · Answer

the solution curves are the smooth curves obtained by joining the slope segments in the slope field : 

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