hws4spring08

# hws4spring08 - Differential Equations/Linear Algebra MTH...

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Unformatted text preview: Differential Equations/Linear Algebra - MTH 2201/2202 Homework 4 Name: 1. yh (t) = c1 ei(-1+ 2)t 02/6/2008 + c2 ei(-1- 2)t 2. yh (t) = c1 et + c2 e-3it 3. (i) yh (x) = c1 + c2 e-4x (ii) yh (x) = c1 e-4x + c2 x e-4x (iii) yh (x) = c1 e -1 x 2 + c2 e 4 x 1 (iv) yh (x) = c1 e-x + c2 ex (v) yh (x) = c1 + c2 e-x + c3 e5x (vi) yh (x) = c1 + c2 e2x + c3 e-2x + c4 cos(2x) + c5 sin(2x) (vii) yh (x) = c1 cos( 3 x) + c2 2 sin( 3 x) + x(c3 2 cos( 3 x) + c4 2 sin( 3 x)) 2 4. (i) yh (x) = 2 e-3x + 3 e2x 5 5 (ii) yh (x) = -1 -3x e 5 + 1 e2x 5 5. yh (x) = cos x + 2 sin x 6. It can shown that satisfies the differential equation y (x) + ky(x) = 0 where k is some constant. 1 7. (i) yh (x) = 2 (3iex 1+3i + e-3ix ) 2 10 (ii) yh (x) = cos( 10x) + sin( 10x) 1 2 8. (x) attains maximum value at x = 0 for all x > 0. Therefore, (x) < for all x > 0. 9. For all values of , all solutions of differential equations tend to zero as t 0. 10. yh (t) = 1 (c1 cos( 53 ln t) + c2 sin( 53 ln t)) t 2 ...
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hws4spring08 - Differential Equations/Linear Algebra MTH...

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