DiffEQ question!! I'm doing Reduction of Order problems, and my book says that we use this method when b^2-4ac = 0. However there is an example that contains the variable t in it, so I am confused as to what exactly the characteristic equation would be.

Question

DiffEQ question!!  I'm doing Reduction of Order problems, and my book says that we use this method when b^2-4ac = 0.  However there is an example that contains the variable t in it, so I am confused as to what exactly the characteristic equation would be.

anonymous · Answer

This is the example: find the fundamental set of solutions$$2t^{2}y^{\prime \prime} + 3ty^{\prime}-y=0$$

anonymous · Answer

read read that http://tutorial.math.lamar.edu/Classes/DE/ReductionofOrder.aspx

anonymous · Answer

the same example

anonymous · Answer

The form your problem takes.$$ax^2\frac{ d^2y }{ dx^2 } + bx \frac{ dy }{ dx }-cy = 0$$

anonymous · Answer

In this case you have t as your independent variable.

anonymous · Answer

Do I include it in the characteristic equation, or should I just not worry about it because I have the$$y_1 = e^{-bt/2a}$$