practicefinalODE2009

practicefinalODE2009 - y 00 + 4 y = 0 using the power...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
Practice Final Exam Professor Cristian Virdol E 1210 Section 001 December 6, 2009 Name: To receive full credit, you must explain your answers. 1 10 2 10 3 10 4 10 5 10 6 10 7 10 8 10 9 10 10 10 Total 100 1
Background image of page 1

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

View Full DocumentRight Arrow Icon
1. Solve the differential equations: (a) y 2 dx + (2 xy - y 2 e y ) dy = 0 (b) cos ty 0 - sin ty = e - 3 t 2
Background image of page 2
2. Find the general solution of the equation: y 00 + 3 y 0 - 4 y = t 2 + t cos t + e 4 t 3
Background image of page 3

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

View Full DocumentRight Arrow Icon
3. Determine (without solving the equation) the largest interval in which the solution of the initial value problem is certain to exist: ± t 2 ( t - 8) y 0 + 1 t - 7 y = e 2 t y (3) = 1 Justify your answer. 4
Background image of page 4
4. Consider the equation y 0 = e y ( y 2 - 5 y + 4). Find the equilibrium points, draw the phase line and classify the equilibrium points as stable, or un- stable. 5
Background image of page 5

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

View Full DocumentRight Arrow Icon
5. Find the general solution of the system x 0 = ± 1 1 4 - 2 ² x + ± - 2 e t e - 3 t ² 6
Background image of page 6
6. Find the general solution of the equation
Background image of page 7

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

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

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

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: y 00 + 4 y = 0 using the power series method. 7 7. Find the solution of the initial value problem y 00 + 4 y = ( t-2 ) , y (0) = 1 , y (0) = 1 8 8. Find the Laplace transform of each of the following functions: (a) t 2 sin 3 t + 3 t 2 + 2 t (b) ( t-5) sin 3 t 9 9. Solve the dierential equation by using the Laplace transform y ( t ) + y ( t ) = Z t sin( t- ) y ( ) d, y (0) = 1 10 10. For the system x = 3-4 1-1 x classify the type of the critical point (0 , 0) and determine whether it is stable, asymptotically stable or unstable. 11...
View Full Document

Page1 / 11

practicefinalODE2009 - y 00 + 4 y = 0 using the power...

This preview shows document pages 1 - 11. Sign up to view the full document.

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