Question

so i have this function:
0.5αe^(0.5t) = 0.5x(t)

can someone explain me what role does e play and how the x comes out?
Topic: first order differential equations

Answer 1

e is a number
x is a function with respect to t.
Those are notations, nothing is special, if you change x by y and t by x, you will see a familiar equation: \(0.5y= 0.5\alpha e^{0.5x}\)

Answer 2

e is a special number whose value is about 2.718 and is sometimes called the exponential constant. The graph of e^x has a special property - that for every point on the graph the gradient of a tangent at that point equals the value of e^x.