Plotting Direction Fields with Mathamatica7

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SUMMARY

This discussion focuses on plotting direction fields of differential equations using Mathematica 7. The specific examples provided are the differential equations y' = 3 - 2y and y' = -1 - 2y. The recommended method for plotting these direction fields is to utilize the StreamPlot function with the syntax StreamPlot[{x'[t], y'[t]}, {x, -a, a}, {y, -b, b}] for general cases and StreamPlot[{1, f[x, y]}, {x, -a, a}, {y, -b, b}] for functions of the form y' = f(x, y).

PREREQUISITES
  • Familiarity with differential equations
  • Basic understanding of Mathematica 7 syntax
  • Knowledge of the StreamPlot function in Mathematica
  • Concept of direction fields in the context of differential equations
NEXT STEPS
  • Explore advanced features of StreamPlot in Mathematica 7
  • Learn about other methods for visualizing differential equations
  • Investigate the implications of direction fields on solution behavior
  • Study the differences between direction fields and phase portraits
USEFUL FOR

Mathematics students, educators, and researchers interested in visualizing differential equations and using Mathematica for mathematical modeling.

khary23
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Can someone please explain to me how one plots direction fields of differential equations in mathamatica 7? Two examples are
y'=3-2y
y'= -1-2y

Thank you
 
Last edited:
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Use StreamPlot[{x'[t],y'[t]},{x,-a,a},{y,-b,b}]

and in the case of just y'=f(x,y), use:

StreamPlot[{1,f[x,y]},{x,-a,a},{y,-b,b}]
 
Thank you!
 

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