Calculating Eigenvalues and Eigenvectors

dvep
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Homework Statement



http://i1225.photobucket.com/albums/ee382/jon_jon_19/Eigen2.jpg

The second term should be De^( - √(5)t), I made a mistake when writing out the question.

The Attempt at a Solution



I worked it out to be

A = 0, B = -1/5, C = 3/10, D = -3/10

answer is 3.09

Is that correct? I have been through my calculations and can find no fault, I just want to make sure I have a good grasp on these questions, thank you.
 
Last edited:
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The link takes me to a moved/deleted picture.
 
gb7nash said:
The link takes me to a moved/deleted picture.

Sorry, I have fixed it now, thanks.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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