Sln1 - Name: (20) 1. Solve the following initial value...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
Name: Page 1 (20) 1. Solve the following initial value problem: z 0 - sin ( x ) z = x 2 ; z (0) = 1 The Integrating factor is : μ ( x ) = e - R sin ( x ) dx = e cos ( x ) therefore the equation can be written as d dx ± e cos ( x ) z ² = x 2 e cos ( x ) and integrating we obtain: e cos ( x ) z = Z x 2 e cos ( x ) dx + c Hence z = e - cos ( x ) Z x 2 e cos ( x ) dx + ce - cos ( x ) but z (0) = 1, thus z = e - cos ( x ) Z x 0 ξ 2 e cos ( ξ ) + e 1 - cos ( x ) or, z = Z x 0 ξ 2 e cos ( ξ ) - cos ( x ) + e 1 - cos ( x )
Background image of page 1

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

View Full DocumentRight Arrow Icon
Name: Page 2 (30) 2. Given the system of two Frst order ODEs x 1 x 2 ! 0 = 0 1 ω 2 - i 2 ω ! x 1 x 2 ! (1) (Note: i = - 1 ) (a) Can you Fnd two linearly independent solutions by diagonalizing the system? (5pt) No because the matrix of the coe±cient has one eigenvalue λ = - with multeplicity 2, and only one belonging vector q 1 = ( iω, ω 2 ) T (b) If not, How would you proceed to Fnd the two linearly independent solutions? (5pt)
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 05/17/2008 for the course MAE 305 taught by Professor Luigimartinelli during the Spring '06 term at Princeton.

Page1 / 4

Sln1 - Name: (20) 1. Solve the following initial value...

This preview shows document pages 1 - 3. Sign up to view the full document.

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