hw2 - ( t ) =-2 by the method of undetermined coecients. 4....

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
ASE 330M Linear System Analysis Unique Number: 12880, Spring 2007 Homework #2 Math Review Date given: February 6, 2007 Date Due: February 15, 2007 1. State whether the following ordinary differential equations are linear or nonlinear. You may assume t to be the independent variable and y ( t ) to be the dependent variable. Also determine the order of each of these differential equation systems: (i) ˙ y ( t ) + y ( t ) = 10 (ii) ¨ y ( t ) + ˙ y ( t ) y ( t ) = x ( t ) (iii) (1 - α y ( t ) + α ˙ y ( t ) = y 3 / 2 ( t ) for α = 1 (iv) ˙ y ( t ) x 2 ( t ) + 1 = y ( t ) + ¨ x ( t ) 2. Solve the following first order ODEs: a) y ( t ) ˙ y ( t ) = sin 2 ωt , ω is a real constant. b) ˙ y ( t ) = y ( t )tanh t You may leave the integration constants within the solution. 3. Solve the first order linear ODE ˙ y ( t ) - 2 y
Background image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ( t ) =-2 by the method of undetermined coecients. 4. Solve the following second linear ordinary dierential equations: a) y ( t ) + y ( t )-2 y ( t ) = 0 subject to y (0) = 1 and y (1) = . b) y ( t )-3 y ( t ) + 8 y ( t ) = 0 subject to y (0) =-1 and y (0) = 0. 5. Consider the following dierential equation y ( t ) + 5 y ( t ) + 6 y ( t ) = x ( t ) + x ( t ) When the function x ( t ) = 6 t 2 is specied, use the method of undetermined coecients to nd the solution y ( t ) assuming initial conditions y (0) = 25 / 18, and y (0) =-2 / 3. 6. Matlab problems B.14, B.22, B.24, and B.39(a) from your textbook. 1...
View Full Document

Ask a homework question - tutors are online