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Unformatted text preview: Assignment #2 Due: At the START of tutorial on June 1, 2011. No late assignments will be accepted. 1. Solve the following differential equations
(a) :cln(:c)% + y 2 21min
(b) w 2 mew + (c) (2x+y+1)f—}g— = 1
(d) ydx + (2mg — e”2y)dy = 0 2. (a) Show that we can transform the differential equation dy 36% into a linear differential equation by using the substitution 2 lug.
(b) Use this method to solve + P($)y = Q($)y1ny d
93—y22x2y + ylny
dcc 3. A Riccati equation is a differential equation with the form / y = 17(90) + qtr)?! + r(w)y2 (a) Suppose we are able to ﬁnd a particular solution yl Show that by using the
substitution y($) = y1(m)+u(x) you can transform a Riccati equation into a Bernoulli’s
equation. (b) Find oneparameter family of solutions for the differential equation d
~2+2$y=l+x2+y2
dm knowing that y1 2 LC is a solution. 4. (a) Find an implicit solution of IVP 2 2 dy y —x
dx 339 ) y< ) f (b) Write the solution explicitly and give the largest interval I over which the solution
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This note was uploaded on 01/15/2012 for the course MATH 201 taught by Professor Steacy during the Fall '10 term at University of Victoria.
 Fall '10
 STEACY

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