Toronto Math Forum
MAT2442014F => MAT244 MathLectures => Topic started by: Boon Yuen Tan on October 01, 2014, 08:23:15 PM

Any idea how to solve this?
$$x^2yâ€²â€²âˆ’9xyâ€²+25y=x^9, \qquad y(1)=7,\quad yâ€²(1)=0. $$
I can't use Wronskian to solve for $y_2$ cause $y_1$ was not given

It is Euler equation. See Handout 4b and the textbook problem 34 on page 166.

Hi, prof,
Just wondering whether it is possible to guess that Ax^9 is a particular solution and then we can solve that A=1/16.
Final, we use reduction of order to find the general solution.

Hi, prof,
Just wondering whether it is possible to guess that $Ax^9$ is a particular solution and then we can solve that $A=1/16$.
Indeed
Final, we use reduction of order to find the general solution.
Would not work. You need to read handout 4b!

You have to first find out the answer
x2y''âˆ’9xy'+25y=0
then that would be your Yc.
Then you need to use the method , variation of parameters from 3.6 to find Yp.
Your final answer would be Y=Yc+Yp

Then you need to use the method , variation of parameters from 3.6 to find Yp.
No need. Guess $y=Ax^9$ is good (because $9$ is not a characteristic root).