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Unformatted text preview: u = y/x to solve the following homogeneous equations. a) y = 3 y 2-x 2 2 xy b) y = 4 y-3 x 2 x-y 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 1-n reduces Bernoulli’s equation to a linear equation. c) Solve y = ±y-σy 3 , ± > , σ > 0. 6. Obtain a continuous solution to the following linear initial value problem with a discon-tinuous coeFcient y + 2 y = g ( x ) , y (0) = 0 , g ( x ) = ( 1 , ≤ x ≤ 1 , , x > 1 ....
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- Winter '09
- Elementary algebra, Initial value problems, linear initial value, Niles A. Pierce