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quiz1.sol

quiz1.sol - x 2 2-– 1 = = y x 29 4 y x 29 = Ay x 29 By x...

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Quiz 1 1. y1(x) and y2(x) are both solutions to a linear differential equation L1, what does that imply about This is also a solution of L1. (Superposition of solutions for linear differential equations). 2. Find the general solution of: 3. Find y(x) such that y(0) = 0, y(Pi/4) = 2 if: ay 1 x ( 29 by 2 x ( 29 + y ' x ( 29 xy x ( 29 + x = λ x ( 29 e x x d e x 2 2 ---- = = dy dx ----- e x 2 2 ---- y x ( 29 xe x 2 2 ---- + xe x 2 2 ---- = e x 2 2 ---- dy y x ( 29 xe x 2 2 ---- xe x 2 2 ---- dx + y x ( 29 e x 2 2 ---- e x 2 2 ---- C y x ( 29
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Unformatted text preview: x 2 2----– 1 + = = y '' x ( 29 4 y x ( 29 + = Ay '' x ( 29 By ' x ( 29 Cy x ( 29 + + ⇒ = B B 2 4 AC – ± – 2 A----------------------------------------2 i ± = y x ( 29 Ae 2 ix Be 2 ix – + = y ( 29 = A B + ⇒ = y π 4-- , 2 iA iB – ⇒ 2 = = A 1 i--= B , 1 i--y x ( 29 ⇒ – e 2 ix e 2 ix – – i-------------------------2 Sin 2 x ( 29 = = =...
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