Solution Sample Assgt SK

Solution Sample Assgt SK - 8. (my creation ) So for this...

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Solution Sample Assgt SK 1. 2.
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3.
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4. SEE in The Zip File 5. SEE THE Zip File 6. SEE in The Zip File
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7. According to me, this one is the more interesting one of the assgt. Why? Well, you will never find the solution for b) using a technique seen in class. . Well you could but it s extremely complicated. So the unique way to find it is to guess the solution! Look carefully at the ode, suppose we remove the y y and y , we will end with 2x x² + x²-2 +2-2x which is equal to 0 Equal to 0 ????? So which function will always be the same even after 2 differentiations? e ^x so we can conclude that y=C1*x² + C2*e^x I advise you to try to resolve it using Wronskian or Reduction of order and you will see that I am right :
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Unformatted text preview: 8. (my creation ) So for this one, you have to remember that ? 2 = 1 ? 2 2 ?? ( )^2 = 1+ ? 2 2 . So lets play with this and the functions to see if their sum could be equal to 0. ? 2 + ? 2 + 1 + 1 ? 2 2 1 2 + cos 2 2 = 0 Which is equivalent to ? 2 + ? 2 + 1 + ? 2 1 2 + cos 2 2 = 0 sin 2 + 1 ? 2 + 1 2 1 + 1 2 cos (2 ) = 0 sin 2 + ? 2 + ? 1 + ? cos (2 ) = 0 With A=0, B=1, C=1/2 and D=1/2 SO (f,g,h,u) are linearly dependent ....
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This note was uploaded on 12/01/2010 for the course MATH 263 taught by Professor Sidneytrudeau during the Fall '09 term at McGill.

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Solution Sample Assgt SK - 8. (my creation ) So for this...

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