The problem is that find the curve, its slope of tangent lines are twice as steep as the ray from the origin. The point is (x,y)
I solve it like this:(dy/dx)=(2y/x) ∫dy/y=∫dx/x
then ln|y|=2lnx+c (c is constant) then y=Ax^2(A=±e^c)
I think that A is ambiguous up to the constant c, and the graph of the curve I'm aiming for, and the graph of the curves is a bunch of parabolas which is undefined at point (0,0). Did I make any mistakes? If I have any one of the curves to the left of y-axis and to the right connected together and take the derivative of it, can I always get dy/dx=2y/x?

Question

The problem is that find the curve, its slope of tangent lines are twice as steep as the ray from the origin. The point is (x,y)
I solve it like this:(dy/dx)=(2y/x)  ∫dy/y=∫dx/x
then ln|y|=2lnx+c (c is constant) then y=Ax^2(A=±e^c)
I think that A is ambiguous up to the constant c, and the graph of the curve I'm aiming for, and the graph of the curves is a bunch of parabolas which is undefined at point (0,0). Did I make any mistakes? If I have any one of the curves to the left of y-axis and to the right connected together and take the derivative of it, can I always get dy/dx=2y/x?

huclogin · Answer

T^T anyone here?

phi · Answer

it sounds right. though the parabola  is defined at (0,0)
however, we may want to exclude the origin?

phi · Answer

because the "ray from the origin" is undefined at (0,0)

huclogin · Answer

|dw:1438353168811:dw|
It's the graph. I can not draw very well.