de5 - Differential Equations Test 5 Solutions Answer FOUR...

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

View Full Document Right Arrow Icon

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

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Differential Equations Test 5 Solutions Answer FOUR questions. Show all working clearly. 1. Find all solutions of d y d x + xy = x. What happens to y as x ? 2. Solve the logistic equation d N d t = rN (1- N/K ) with N (0) = M (the constants r,K,M being positive). 3. Solve the IVP y 00- 2 y + y = 2 e t ; y (0) = 0 ,y (0) = 0 . 4. Solve the mechanical vibration problem m x + kx = F cos t ; x (0) = a, x (0) = 0 given that = p k/m . 5. Calculate the Laplace transforms of the following functions of t : (i) e at , (ii) sin t , (iii) cos t , (iv) t . Solutions : 1. The given equation is linear (and in standard form) with integrating factor exp( Z x d x ) = exp( x 2 / 2) , multplication of the DE by which yields d d x [ y exp( x 2 / 2)] = x exp( x 2 / 2) so that y exp( x 2 / 2) = Z x exp( x 2 / 2)d x = exp( x 2 / 2) + k or y = 1 + k exp(- x 2 / 2) . Of course, this makes it clear that y 1 as x ....
View Full Document

This note was uploaded on 11/12/2011 for the course MAP 2302 taught by Professor Tuncer during the Fall '08 term at University of Florida.

Page1 / 3

de5 - Differential Equations Test 5 Solutions Answer FOUR...

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

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