Consider the Initial Value Problem consisting of the ODE and the Initial Condition given below. dy...

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Consider the Initial Value Problem consisting of the ODE and the Initial Condition given below. dy dt y(t=0) = 2 a) State whether the ODE is linear or nonlinear. b) Express the ODE as an algebraic equation using Backward differencing for the approximation of the derivative at the time level t, where i+1 represents the time index at the next iteration. c) Solve for y(t=0.5) using Backward Euler method with At = 0.25 =-y*et Consider the Initial Value Problem consisting of the ODE and the Initial Condition given below. dy dt y(t=0) = 2 a) State whether the ODE is linear or nonlinear. b) Express the ODE as an algebraic equation using Backward differencing for the approximation of the derivative at the time level t, where i+1 represents the time index at the next iteration. c) Solve for y(t=0.5) using Backward Euler method with At = 0.25 =-y*et