midterm2-A-solution-public

# 5 marks find the general solution to y 4y 4y e 2x x

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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.

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