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
 Winter '09
 NilesA.Pierce
 Elementary algebra, Initial value problems, linear initial value, Niles A. Pierce

Click to edit the document details