Cauchy-Euler equation - Wikipedia, the free encyclopedia
One way to solve it is to set (if use instead)
Let
Then and
We have that:
So instead you need to solve
The question is find the solution of:
clearly the coefficients in what i would write down to be the auxilliary equation are not constants. Ive been told by my solution to use y= but i dont see how this gives(in the solutions)
giving m=4 or m=-2. and the corrosponding complementary function. Does anyone have any ideas or could show me how the method actually cancels out the non constant coefficeints? thanks. oh i think you are supposed to use liebnitz?? not sure
Cauchy-Euler equation - Wikipedia, the free encyclopedia
One way to solve it is to set (if use instead)
Let
Then and
We have that:
So instead you need to solve
The complete equation is...
(1)
Both and are solution of the incomplete equation and they are also linearly independent, so that the general integral of the incomplete equation is ...
(2)
With little patience you find that is solution of (1) , so that the general integral of (1) is...
(3)
Kind regards
You have to consider as first step the searching ot solution of the incomplete equation...
(1)
If you suppose that is solution of (1) , you find by simple substitution in (1) that that is true for and . But they are linearly independent so that the general integral of (1) is...
(2)
The first step is terminated. The second step consists in searching a particular solution of the complete equation... not a very difficult task...
Kind regards