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Consider the initial value problem given by y′ = 2y−1 with the initial condition y(0) = 1. (a) Use Euler's method to find an approximate value of the solution at t = 2 using a step size of 0.5 (that is, Δt = 0.5 ). (b) Solve for the exact value of the solution at t = 2 by finding a particular solution to the original differential equation and then finding y(2). (c) In what way could we have altered the method in part (a) to get a solution value closer to the exact solution at t = 2?

Consider the initial value problem given by y′ = 2y−1 with the initial condition y(0) = 1. (a) Use Euler's method to find an approximate value of the solution at t = 2 using a step size of 0.5 (that is, Δt = 0.5 ). (b) Solve for the exact value of the solution at t = 2 by finding a particular solution to the original differential equation and then finding y(2). (c) In what way could we have altered the method in part (a) to get a solution value closer to the exact solution at t = 2?

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  1. (10 points) Consider the initial value problem given by
y ′ = 2 y − 1
with the initial condition y ( 0 ) = 1 . (a) Use Euler's method to find an approximate value of the solution at t = 2 using a step size of 0.5 (that is, Δ t = 0.5 ). (b) Solve for the exact value of the solution at t = 2 by finding a particular solution to the original differential equation and then finding y ( 2 ) . (c) In what way could we have altered the method in part (a) to get a solution value closer to the exact solution at t = 2 ?

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