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Cylinder
The below equation is the common equation of a cylinder.
x2 /a2 + y2/b2 = 1
This is known as a cylinder whose cross section is an ellipse. If a = b we comprise a cylinder whose cross section is a circle. We will be dealing with those types of cylinders more than the general form thus the equation of a cylinder along with a circular cross section is,
x2 + y2 = r2
Here is a diagram of typical cylinder along with an ellipse cross section.
In the diagram the cylinder will be centered on the axis corresponding to the variable which does not appear in the equation.
Be cautious to not confuse this with a circle. In two dimensions it is a circle, although in three dimensions (3D) it is a cylinder.
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The actual solution is the specific solution to a differential equation which not only satisfies the differential equation, although also satisfies the specified initial conditions
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