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October 13th, 2015, 06:42 PM   #1
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Thumbs up Planar Linear Systems

Give an example of a system of differential equations for which (t, 1) is
a solution. Sketch the direction field for this system. What is the general
solution of this system?

I am trying to solve this problem for home work, but I couldn't do it, any help from the members. Thanks in advance

Regards,
Viru
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October 28th, 2015, 05:25 AM   #2
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What, exactly, is the difficulty? You are asked to find a system of differential equations in say, x(t), y(t), such that x(t)= 1, y(t)= t is a solution. I would think it obvious that x'= 0, y'= 1 would work. The "direction field" is a diagram where, at every (x, y) point, a short line segment is given showing the direction of a tangent to the solution graph at that point. Here, because of the "x'= 0" condition every such tangent line is vertical!
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