hws4spring08

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

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

Page1 / 2

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online