skech the direction field of the differential equation dx/dt =-2t. Any idea please?

Question

anonymous · Answer

First, draw your axes. Then, find the slope of a potential curve by plugging in various values of $t$.

For example, when $t=2$, the slope of the curve $x(t)$ is given by $\dfrac{dx}{dt}\bigg|_{t=2}=-2(2)=-4$.

Since the slope depends only on $t$, the slope at any point $(2,x(2))$ is -4.
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The drawing's far from perfect, but you get the idea.

anonymous · Answer

Now try a different point, maybe $t=0$. The slope is $\dfrac{dx}{dt}\bigg|_{t=0}=-2(0)=0$, so along the $x(t)$-axis, every solution curve will have a horizontal tangent line:
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