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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
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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 °±? 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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