Finding slope fields using Euler method

[Philip Wong]

hi guys,

can someone give me a quick tutorial on how to solve and explain to me the concept of slope field of the following differential equation:
sketch the slope field for dy/dt = 2t+1
showing the solution y=t^2+t-4, which satisfies the initial condition y(-2)= -2


Also how to use the Euler's method to solve the slope field of the above differential condition.

thanks!

 

[HallsofIvy]

Choose a number of points in a ty- coordinate system (t is the horizontal axis, y the vertical axis. At each (t, y) point, draw a short line segment having slope 2t+ 1. Since that does not depend on y, you can do that by marking lines with the same slope in a vertical "stack".

Now, starting at the point (-2, -2), draw a curve that is always tangent to those line (use the short lines to give the direction at each point). The curve should look like $y= t^2+ t- 4.<br /> <br /> You <b>don't</b> use Euler's method to "solve the slope field". Euler's method is used to find a numerical approximation to the solution to a differential equation problem.$