Homework Statement
Use the power series to solve the following differential equations, state the first four terms of the two independent solutions.
3xy'' + y' - y = 0
Homework Equations
The power series.
The Attempt at a Solution
How do I get two independent solutions out of this? All...
Let the Wronskian between the functions f and g to be 3e^{4t}, if f(t) = e^{2t}, then what is g(t)?
So the Wronskian setup is pretty easy
W(t) = fg' - f'g = 3e^{4t}
f = e^{2t}
f' = 2e^{2t}
So plugging it in I would get:
e^{2t}g' - 2e^{2t}g = 3e^{4t}
Which results in
g' - 2g...