Question
Plot the direction field for the differential equation by hand. Do this by drawing short lines of the appropriate slope centered at each of the integer valued coordinates $(t, y)$, where $-2 \leq t \leq 2$ and $-1 \leq y \leq 1$.$$y^{\prime}=y+t$$
Step 1
This will give us a total of 15 points: $$ (-2, -1), (-2, 0), (-2, 1), (-1, -1), (-1, 0), (-1, 1), (0, -1), (0, 0), (0, 1), (1, -1), (1, 0), (1, 1), (2, -1), (2, 0), (2, 1) $$ Show more…
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Plot a direction field for the following differential equation with a graphing utility. Then find the solutions that are constant and determine which initial conditions $y(0)=A$ lead to solutions that are increasing in time. $$y^{\prime}(t)=t(y-1), \quad 0 \leq t \leq 2,0 \leq y \leq 2$$
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