ma266-suppl-f10

ma266-suppl-f10 - Supplementary Problems A For what value(s...

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Supplementary Problems A. For what value(s) of A , if any, will y = Ate - 2 t be a solution of the differential equation 2 y 0 + 4 y = 3 e - 2 t ? For what value(s) of B , if any, will y = Be - 2 t be a solution? B. Using the substitution u ( x ) = y + x , solve the differential equation dy dx = ( y + x ) 2 . C. Using the substitution u ( x ) = y 3 , solve the differential equation y 2 dy dx + y 3 x = 2 x 2 ( x > 0). D. Find the explicit solution of the Separable Equation dy dt = y 2 - 4 y , y (0) = 8. What is the largest open interval containing t = 0 for which the solution is defined? E. The graph of F ( y ) vs y is as shown: - 6 - 4 - 2 2 4 6 8 - 3 3 w y w = F ( y ) (a) Find the equilibrium solutions of the autonomous differential equation dy dt = F ( y ). (b) Determine the stability of each equilibrium solution. F. Solve the differential equation dw dt = 2 tw w 2 - t 2 G. (a) If y 0 = - 2 y + e - t , y (0) = 1 then compute y (1). (b) Experiment using the Euler Method ( eul ) with step sizes of the form h = 1 /n to find the smallest integer n which will give a value y n that approximates the above true solution at t = 1 within 0 . 05.
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