midterm2-B-solution-public

5 marks find the general solution to y 2y y ex x

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Unformatted text preview: te, u2 = x2 + C , • determine C using the initial condition: when x = 1, u(1) = y ￿ (1) = 1, 12 = 1 + C , C = 0, so, u2 = x2 • isolate u = y ￿ , y ￿ = u = ±x, Note that y ￿ > 0 at x = 1, so we pick the positive branch, y￿ = x • Integrate, y = 1 x2 + c1 , determine c1 using the initial condition, y (1) = 1 12 + c1 = 1, 2 2 c1 = 1 2 1 1 y = x2 + 2 2 4. [5 marks] Find the general solution to y ￿￿ − 2y ￿ + y = ex . 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 − 2λ + 1 = 0, λ = 1, repeated roots. – two linearly independent solutio...
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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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