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Unformatted text preview: c) Find the time required for half the salt to leave the tank. Dont compute the decimal approximation here. 4) True  False. Tell whether the following statements are true or false. Give a reason for your answer. a) The ODE (y cosx + 2x e y ) + (sinx +x 2 e y1) y(x) = 0 is exact. b) If f and f y are continuous in a rectangle xx  a, yy  b, then there is some interval on which the initial value problem y(x) = f(x,y), f(x )=y , cannot have 2 distinct solutions. c) The logistic equation y(x) = ry(1y/K) has two equilibrium solutions y = K and y = 0. The first of these is stable while the second is unstable. 5) a) Find a fundamental set of solutions for y + y  2y = 0. b) Compute the Wronskian determinant of the fundamental set from part a). c) Solve the initial value problem: y + y 2y = 0, y(0)=2, y(0) = 3. aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa...
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 Spring '06
 Mohanty
 Math

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