Unfortunately, you have not shared the point through which the curve passes. Would you please do that now.
Just supposing that the graph passes through the point (2,2) (which I have invented as an example):
Write the differential equation dy/dx = 2y. Rewrite this as dy/y=2dx. Integrating both sides, ln|y|=2x+ln|c| (where c is just a constant of integration).
Solving for y: ln|y|-ln|c|=2x, or ln|y/c|=2x
then y/c=e^(2x), or y=c*e^(2x). What is the value of c? To determine this, let x=2 and y=2:
2=c*e^(2[2]) after substituting the coordinates of the point (2,2). Then
2=ce^4, or c=1/[e^4].
Substituting this c into the solution,
y= (1/[e^4])e^[2x]
This solution can be used as is, or you could try simplifying it.
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Note that if your graph goes through some point other than (2,2), the correct answer to this problem will be different.
