Solution Sample Assgt SK

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

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4. SEE in The Zip File 5. SEE THE Zip File 6. SEE in The Zip File
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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