Differential Equations

Question

The letter y appears in two places in the differential equation dy/dt = 0.3y. Is it appropriate to
think of both occurrences of y as function of t? Explain.

Answer 1

It is the same y.  This is an example of a separable differential equation.

 

dy/dt = 0.3y

 

dy/y = 0.3dt

 

lny = 0.3t + c

 

Let c = lnK, where K is a constant

 

lny = 0.3t + lnK

 

y = Ke^0.3t = y(t)

 

Note that y(0) = K

 

y(t) = y(0) e^0.3t