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Solution Sample Assgt SK

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

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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
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 °±? ²³ 2 = 1 − ´?µ 2 ∗¶³ 2 ??µ ( ² )^2 = 1+ ´?µ 2 ∗¶³ 2 . So let’s play with this and the functions to see if their sum could be equal to 0. − µ±? ²³ 2 + ´?µ ²³ 2 ³ + 1 + 1 − ´?µ 2 ∗ ¶³ 2 − 1 2 + cos 2 ²³ 2 = 0 Which is equivalent to − µ±? ²³ 2 + ´?µ ²³ 2 ³ + 1 + µ±? ²³ 2 − 1 2 + cos 2 ²³ 2 = 0 ∗ sin ²³ 2 + 1 ∗ ´?µ ²³ 2 ³ + 1 2 ∗ 1 + · 1 2 ¸ ∗ cos ⁡ (2 ² ) = 0 ¹ ∗ sin ²³ 2 + º ∗ ´?µ ²³ 2 ³ + ? ∗ 1 + ? ∗ cos ⁡ (2 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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