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# First order differential FP3 watch

1. I have the equation dy/dx+y=x^2 and the question asks show that if the solution curve has a stationary point it lies on the line y=x^2.

I can calculate that the solution curve is:

y=x^2-2x+2+c/e^x

and from this if I assume that c=0, setting dy/dx=0 I can find that x=1,y=1 at a sp. This lies on y=x^2. Is this sufficient evidence or is it lacking in proof?

Also why would any solution curve cut the line y=x+1 at right angles?
2. I would suggest that the easiest way to show the answer is simply from the equation you are given, set dy/dx to 0 and you get 0 + y = x^2 at any stationary point

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