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A slope field for the differential equation dy dt = 0.5(y + t) is shown below. (a) For the initial condition of y(0) = 1, sketch on the slope field what you think the solution function will look like. (b) Estimate, using your sketch, the value of y(2). (c) Use Euler's method with a step size of 0.5 to predict the value of y(2) with the initial condition y(0) = 1.

A slope field for the differential equation dy dt = 0.5(y + t) is shown below. (a) For the initial condition of y(0) = 1, sketch on the slope field what you think the solution function will look like. (b) Estimate, using your sketch, the value of y(2). (c) Use Euler's method with a step size of 0.5 to predict the value of y(2) with the initial condition y(0) = 1.

Image text
A slope field for the differential equation
d y d t = 0.5 ( y + t )
is shown below. (a) For the initial condition of y ( 0 ) = 1 , sketch on the slope field what you think the solution function will look like. (b) Estimate, using your sketch, the value of y ( 2 ) . (c) Use Euler's method with a step size of 0.5 to predict the value of y ( 2 ) with the initial condition y ( 0 ) = 1 .

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