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Unformatted text preview: ), W ( y 1 ,y 2 )( t ) = y 1 ( t ) y 2 ( t )-y 1 ( t ) y 2 ( t ) 6 = 0. Show that the initial value problem y 00 + py + qy = 0; y ( t ) = y , y ( t ) = y has a unique solution in the form y ( t ) = c 1 y 1 ( t ) + c 2 y 2 ( t ). 1 4. Find the general solution to y 00-y + y = cos(2 t ) . 5. Using Eulers method, with t = 1 / 2, nd an approximate value for y (1), where y + 4 y = t ; y (0) = 1. 6. For the autonomous DE dx dt = 1-x 2 , identify the critical points and classify them as stable or unstable. Plot (qualitatively) some representative solutions (dont forget to include the equilibrium solutions) in the t-x plane below. 2...
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