<exercise masterit-seed="1233" masterit-slug="F1" masterit-name="Direction fields for first-order ODEs">
<statement>
<p>
Use <url href="https://sagecell.sagemath.org/"/> to run the SageMath code
<c>t,y = var('t y'); plot_slope_field(sin(t+y), (t,-5,5), (y,-5,5))</c>
producing the direction field for the ODE <m> {y'} = \sin\left({y} + t\right) </m>.
</p>
<p>
Let <m>y_p</m> be the solution to the following IVP.
Explain how to use its direction field to approximate the
value of <m>y_p</m> at <m>t= -2 </m>.
</p>
<me> {y'} = \sin\left({y} + t\right) \hspace{2em}
y( 0 )= 1 </me>
</statement>
<answer>
<me>y_p( -2 )\approx 1.0 </me>
</answer>
</exercise>
