2. (6 points) Consider the differential equation (1+2)y' - ty = 2t. (a) Using Python, plot...

 

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2. (6 points) Consider the differential equation (1+2)y' - ty = 2t. (a) Using Python, plot the slope field for the differential equation. On the slope field, sketch a few solutions for different initial conditions. Describe what appears to happen as too. If the behavior depends on the initial value of y, then describe this dependence. (b) Find the general solution to the differential equation. (c) Find the solution with initial condition y(0) =yo (o is just some number). (d) Take the limit as t (the limit will depend on the value of yo). Was your guess in part (a) correct? 2. (6 points) Consider the differential equation (1+2)y' - ty = 2t. (a) Using Python, plot the slope field for the differential equation. On the slope field, sketch a few solutions for different initial conditions. Describe what appears to happen as too. If the behavior depends on the initial value of y, then describe this dependence. (b) Find the general solution to the differential equation. (c) Find the solution with initial condition y(0) =yo (o is just some number). (d) Take the limit as t (the limit will depend on the value of yo). Was your guess in part (a) correct?