This preview shows pages 1–2. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: u = y/x to solve the following homogeneous equations. a) y = 3 y 2x 2 2 xy b) y = 4 y3 x 2 xy 5. The Bernoulli equation y + p ( x ) y = q ( x ) y n is an example of a nonlinear ODE that can be made linear by a change of dependent variable. a) Solve the equation for n = 1. b) Show that if n is an integer larger than one, the substitution u = y 1n reduces Bernoulli’s equation to a linear equation. c) Solve y = ±yσy 3 , ± > , σ > 0. 6. Obtain a continuous solution to the following linear initial value problem with a discontinuous coeFcient y + 2 y = g ( x ) , y (0) = 0 , g ( x ) = ( 1 , ≤ x ≤ 1 , , x > 1 ....
View
Full
Document
This note was uploaded on 01/08/2011 for the course ACM 95b taught by Professor Nilesa.pierce during the Winter '09 term at Caltech.
 Winter '09
 NilesA.Pierce

Click to edit the document details