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Unformatted text preview: u, udu = 4xdx
• Integrate, u2 = 4x2 + C , • determine C using the initial condition: when x = 1, u(1) = y (1) = 2, 22 = 4(1) + C ,
C = 0, so, u2 = 4x2
• isolate u = y , y = u = ±2x, Note that y > 0 at x = 1, so we pick the positive branch,
y = 2x
• Integrate, y = x2 + c1 , determine c1 using the initial condition, y (1) = 12 + c1 = 5,
c1 = 4
• So, y = x2 + 4
4. [5 marks] Find the general solution to y − 4y + 4y = e 2x
.
x • This is not in a form that the undetermined coeﬃcients method applies. Use variation
of parameters
• The solution of homogeneous part: – The auxiliary equation: λ2 − 4λ + 4 = 0, λ = 2, repeated roots.
– two linearly independent solutions:...
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This test prep was uploaded on 03/31/2014 for the course MATH 201 taught by Professor Steacy during the Fall '10 term at University of Victoria.
 Fall '10
 STEACY
 Math

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