I am trying to use reduction of order to find the solution to x^2y''-7xy'+6y=0. Y1=x^4. I found y2(x) y2''(x) and y2'(x0 and plugged them in to get 18x^4v-3x^5v'+x^6v''. But I think thats wrong. Ca anyone help?

Question

experimentx · Answer

try this http://en.wikipedia.org/wiki/Cauchy%E2%80%93Euler_equation

anonymous · Answer

If u sub x^4 in the given de, it doesn't come out to 0 (-10x^4).

After doing the reduction I get

-10x^4 + x^5v' +x^6v''   so

I think there is a mistake in the question.

anonymous · Answer

It's actually 16y. But I'm still stuck!

anonymous · Answer

Did u get 

x^5v' +x^6v''

as well?

anonymous · Answer

yes

anonymous · Answer

So I guess now u just put w = v' -> w' = v'' to get a first oder de