Preliminary Analysis

We begin the analysis of this problem with the slope field.

> VAR := { y(t) }; # specify the variables in the model

> DOMAIN := t = 0 .. 1; # specify a reasonable interval for the independent variable

> RANGE := y = -0.1 .. 1 ; # specify a reasonable interval for the dependent variable

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> plotSLOPE := DEplot( MODEL, VAR, DOMAIN, RANGE, arrows = MEDIUM ):

> plotSLOPE;

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When the solution curve through the specified initial condition is added, the picture looks like

> DEplot( MODEL, VAR, DOMAIN, RANGE, [ [IC] ], linecolor = BLUE, arrows = MEDIUM );

Notice how the solution curve is always tangentiala to the slope field. (This is a good way to check that your "answer" is reasonable.)

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Even though it is not asked for in this problem, let's see what Maple can do for an analytic solution.

> SOLN := dsolve( { MODEL, IC }, VAR );

UGH! No wonder we haven't spent more time worrying about explicit solutions!!!

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