Math 350 Differential Equations Homework Questions 6-1
Submit nothing! Questions only for midterm review purposes. . .
6
Nonlinear Systems and Phenomena
6.1
Stability and the Phase Plane
1, 2 Find all the equilibrium solutions x (t) = x0 to the given seco
Math 350: Differential Equations Midterm 2
Total marks = 50 (per question in brackets)
Remember to explain your answers and show your working for full credit!
Question
1
2
3
4
Total
Marks
/20
/10
/5
/15
/50
1 Consider the system of linear equations
x = x
Math 350 Differential Equations Homework Questions 7
Submit the * questions on Thursday of Week 12 (Nov 14th) some, or all will be graded. . .
6.2
Linear and Almost Linear Systems - part II
1, 2 Identify the type of the critical point (0, 0) of the given
Math 350: Differential Equations Midterm 1 (v1)
Total marks = 50 (per question in brackets)
Explain your answers and show your working for full credit
Feel free to leave your solutions as integrals or in implicit form if no simpler expression is available
Math 350 Differential Equations Homework Questions 8
Submit the * questions on Tuesday of Week 14 (Nov 26th) some, or all will be graded. . .
7.1
Laplace Transforms and Inverse Transforms
1 Apply the denition to nd directly the Laplace transform of f (t)
Math 350 Differential Equations Homework Questions 3
Submit the * questions on Thursday of Week 4 (Sept 19th) some, or all will be graded. . .
2.4
Eulers Method
13 An initial value problem and its exact solution y( x ) are given. Apply Eulers method twice
Math 350 Differential Equations Homework Questions 5
Submit the * questions on Thursday of Week 8 (Oct 17th) some, or all will be graded. . .
3.6
Forced Oscillations and Resonance
1 Find the steady periodic solution xsp (t) = C cos(t ) of the equation
x +
Math 350 Differential Equations Homework Questions 4
Submit the * questions on Thursday of Week 7 (Oct 10th) some, or all will be graded. . .
3.4
Mechanical Vibrations
1 * A body with mass 250 g is attached to the end of a spring that is stretched 20 cm b
Math 350 Differential Equations Homework Questions 6
Submit the * questions on Thursday of Week 8 (Oct 24th) some, or all will be graded. . .
5
Linear Systems of Differential Equations
5.1
Matrices and Linear Systems
1, 2 Write the system in the form x =
Math 350 Differential Equations Homework Questions 3-1
Submit nothing! Questions only for midterm review purposes. . .
3.2
General Solutions of Linear Equations
1 Show that the functions f ( x ) = 17, g( x ) = 2 sin2 x, h( x ) = 3 cos2 x are linearly depe
Math 350 Differential Equations Homework Questions 2
Submit the * questions on Thursday of Week 3 (Sept 12th) some, or all will be graded. . .
2
Mathematical Models and Numerical Methods
2.1
Population Models
1, 2 Separate variables and use partial fracti
Math 350: Differential Equations Midterm 1 (v2)
Total marks = 50 (per question in brackets)
Explain your answers and show your working for full credit
Feel free to leave your solutions as integrals or in implicit form if no simpler expression is available