anonymous
  • anonymous
ODE problem confused!
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
1 Attachment
anonymous
  • anonymous
Confused on b(ii)
anonymous
  • anonymous
I'm not sure what to do.

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More answers

anonymous
  • anonymous
I have to find u somehow I reckon, not 100% though.
anonymous
  • anonymous
Hmm I believe you just have to show that the identity is valid, because the roots are identical.
anonymous
  • anonymous
pretty similar to the part before it
anonymous
  • anonymous
But I will try first.
anonymous
  • anonymous
the other solution will have an additional x infront of it I am not mistaken.
anonymous
  • anonymous
juts plug it in and see what happens
experimentX
  • experimentX
http://en.wikipedia.org/wiki/Reduction_of_order
anonymous
  • anonymous
If it's double roots then yes there's extra x in the solution.
anonymous
  • anonymous
I'm still not sure what should I do first.
anonymous
  • anonymous
I don't know what u is.
experimentX
  • experimentX
assume that \( x(t) = u(t) x_1(t) \) is another solution ... find the value of u(t) ... so that you have complete solution.
anonymous
  • anonymous
Still lost...
anonymous
  • anonymous
@experimentX I genuinely don't know where to start.
experimentX
  • experimentX
i think there is an example in the wikipedia ... in the link i posted above.
anonymous
  • anonymous
If I understand this problem then they just want you to check what happens if you substitute back their provided result. I believe their are trying to introduce you to the method of Reduction of Order You will get a result in the form of \[ \Large u(x)=d_1x+d_2 \] where \(d_1, d_2\) are constant. The second solution is of the form \[ \Large y_2(x)=u(x)e^{\frac{x}{2}}\] So you can use superposition to get the general solution.
experimentX
  • experimentX
|dw:1344360084786:dw|
anonymous
  • anonymous
Note that \[ \Large 4r^2-4r+1=0 \] Has a discriminant of zero.
anonymous
  • anonymous
Pardon me if I was interrupting something in here, OpenStudy lags horribly for me today so I hit the post button before it crashes me again (-:
anonymous
  • anonymous
and how does that prove it equals 0?
anonymous
  • anonymous
Yeah it pretty bad this week
anonymous
  • anonymous
What I understand so far, we need to sub ux into equation 4
anonymous
  • anonymous
\[4\left( u''e^{\frac{t}{2}} + \frac{1}{2}e^{\frac{t}{2}}u' + \frac{1}{4}e^{\frac{t}{2}}u + \frac{1}{2}u'e^{\frac{t}{2}}\right) -4 \left(u' e^{\frac{t}{2}}+ \frac{1}{2}e^{\frac{t}{2}}u \right)+ ue^{\frac{t}{2}}=0\]
anonymous
  • anonymous
Divide by \( \large e^{\frac{t}{2}} \) and then see what happens when you bring it all together.

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