DE2summer07

DE2summer07 - MTH 2201 Differential Equations Homework 2...

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Unformatted text preview: MTH 2201 Differential Equations Homework 2 : Linear Equations Spring 2008 1. Find the general solution of the given ODE and give the largest interval on which the solution is defined. dy (i) y + 3t2 y = t2 . (ii) t - y = t2 sin t. dt dy 2 t (ii) t y + t(t + 2)y = e . (iv) (cos t) + (sin t)y = 1. dt dr (v) + r sec = cos d 2. Find the solutions to the following IVPs : dT = K(T - Tm ), T (0) = T0 , K, Tm , T0 are constants. (i) dt dx (ii) (t + 1) + x = ln t, x(1) = 10. dt dy 1, 0 t 1 (iii) + y = f (t), f (t) = , y(0) = 1. -1 t > 1 dt 3. Solve dy - 2ty = 2, dt y(0) = 1, in terms of erf (t). y(0) = , in terms of erf c(t). 2 dy 4. Solve - 2ty = -1, dt t sin u 5. Define Si(t) = du. u 0 Show that the solution of the IVP t3 y + 2t2 y = 10 sin t, y(1) = 0 -2 is y(t) = 10t [Si(t) - Si(1)]. 1 ...
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