{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

midterm2-B-solution-public

# midterm2-B-solution-public - Math 201 Fall 2011 Midterm...

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

Math 201 Fall 2011 Midterm Exam 2 (B) October 28, 2011 1. [5 marks] Find the solution of the initial value problem y °° 2 y ° +2 y =0 , y (0) = 1 , y ° (0) = 0 The auxiliary equation λ 2 2 λ +2=0 , λ =1 ± i . So the two linearly independent solutions are y 1 = e x cos x , y 2 = e x sin x The general solution is y = c 1 y 1 + c 2 y 2 = c 1 e x cos x + c 2 e x sin x We use the initial values to determine c 1 and c 2 y (0) = c 1 y ° = c 1 e x cos x c 1 e x sin x + c 2 e x sin x + c 2 e x cos x , y ° (0) = c 1 + c 2 , c 2 = c 1 = 1 So, y = e x cos x e x sin x 2. [5 marks] Find the general solution to y °° y ° 2 y = 6 e x The general solution to the homogeneous part: Auxiliary equation: λ 2 λ 2=0 , λ = 1 , λ =2 Two linearly independent solutions: y 1 = e x , y 2 = e 2 x Guess for a particular solution: y p = axe x (we need x multiplied to e x because e x is aso lut iontothehomogeneouspart) .

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 3

midterm2-B-solution-public - Math 201 Fall 2011 Midterm...

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

View Full Document
Ask a homework question - tutors are online