Consider the differential equation y' = y + ty. (a) Use Euler's method with a step...

 

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Consider the differential equation y' = y + ty. (a) Use Euler's method with a step size of At 0.1 to estimate y(.5), where y(x) is a solution to the differential equation with y(0) = 1. (b) Solve the differential equation using either separation of variables or by writing it as a first order linear equation and multiplying by an appropriate integrating factor (as in the previous exercise). (c) Draw a plot which demonstrates the solutions to the previous two parts. Your plot should show the graph of the solution to part (b) for 0 ≤ t ≤.5 as compared with the approximate solution obtained in part (a) illustrating Euler's method. Consider the differential equation y' = y + ty. (a) Use Euler's method with a step size of At 0.1 to estimate y(.5), where y(x) is a solution to the differential equation with y(0) = 1. (b) Solve the differential equation using either separation of variables or by writing it as a first order linear equation and multiplying by an appropriate integrating factor (as in the previous exercise). (c) Draw a plot which demonstrates the solutions to the previous two parts. Your plot should show the graph of the solution to part (b) for 0 ≤ t ≤.5 as compared with the approximate solution obtained in part (a) illustrating Euler's method.