Register to reply

Reduction of Order

by vipertongn
Tags: order, reduction
Share this thread:
Aug19-10, 05:18 PM
P: 98
1. The problem statement, all variables and given/known data

solve y"-4y'+4y=0 y1=e^(2x) using reduction of order

3. The attempt at a solution

I then substitute that into the original equation to get


simplify to get

from here I do not know what to do...I do know the answer is suppose to be xe^2x, but I don't know how that is done.
Phys.Org News Partner Science news on
Experts defend operational earthquake forecasting, counter critiques
EU urged to convert TV frequencies to mobile broadband
Sierra Nevada freshwater runoff could drop 26 percent by 2100
Aug19-10, 06:17 PM
HW Helper
P: 6,202
From u"e2x=0, you can divide by e2x and solve u''=0.
Aug19-10, 06:38 PM
P: 98 then u"=0 makes u'=c and then later u=xc1+c2 and

but what then? how do I solve for c1 and c2?

Aug19-10, 06:43 PM
P: 21,314
Reduction of Order

You need initial conditions in order to solve for the constants c1 and c2.
Aug19-10, 06:49 PM
P: 98
however, in my solutions manual it says the solution comes out to be xe^2x, and I have no idea how that came to be. except for the use of this equation
y2=y1S e^(-SP(x)dx)/y1^2 dx
Aug19-10, 07:36 PM
P: 21,314
The general solution of your diff. equation is y = c1e^(2x) + c2xe^(2), for any values of c1 and c2. The simplest pair of linearly independent solutions is the pair with c1 = c2 = 1, so maybe they just arbitrarily chose that one.

Register to reply

Related Discussions
2nd order differential equation using reduction of order Calculus & Beyond Homework 7
Reduction of order (2nd order linear ODE homogeneous ODE) Calculus & Beyond Homework 10
Reduction of order Calculus & Beyond Homework 1
ODE - Reduction of order Calculus & Beyond Homework 1