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Exercises

For each exercise, make a note of the problem, (both the differential equation and plot bounds), then switch toÌýMathematicaÌýand create the slope field by clicking on the "try it" link. Remember, you'll be entering your own parameters this time. When you return you may verify your answer and read any applicable comments about the problem by clicking on the "discuss it" link.Ìý(Only choose this option once you've done the problem yourself in Mathematica.)

1. dy/dxÌý=Ìýx, on the region -3 ≤ÌýxÌý≤ 3, and -3 ≤ÌýyÌý≤ 3, no arrow-heads, including axes, default vector grid
   • First youÌýtry it!
   • Then weÌýdiscuss it!
2. dy/dxÌý= sinÌýx, on the region -2Ï€ ≤ÌýxÌý≤ 2Ï€, and -5 ≤ÌýyÌý≤ 5, no arrow-heads, including axes, 25 X 25 vector grid
   • First youÌýtry it!
   • Then weÌýdiscuss it!
3. dy/dxÌý=Ìýe^-x, on the region -1 ≤ÌýxÌý≤ 1, and 0 ≤ÌýyÌý≤ 4, no arrow-heads, including axes, 20 X 20 vector grid
   • First youÌýtry it!
   • Then weÌýdiscuss it!
4. dy/dxÌý=Ìýx²Ìýe^-x, on the region -1 ≤ÌýxÌý≤ 2, and -1 ≤ÌýyÌý≤ 1, no arrow-heads, including axes, default vector grid
   • First youÌýtry it!
   • Then weÌýdiscuss it!

Hopefully you had some success doing these exercises by yourself. Now that we've had some practice with this general class of differential equation it's time to make someÌýgeneral observations.