If you plug in the slope field dy/dx = x^2/y^2 into this generator, http://www.math.rutgers.edu/~sontag/...OdeApplet.html
How do you interpret that graph? Is that straight line that runs through the origin part of the solution?
If you plug in the slope field dy/dx = x^2/y^2 into this generator, http://www.math.rutgers.edu/~sontag/...OdeApplet.html
How do you interpret that graph? Is that straight line that runs through the origin part of the solution?
One way to think about slope fields is to imagine them like currents on a river. If you drop a cork into the river at a certin point (the initial condition) where will the cork go? The path of the cork will always be parallel to the flow lines. On the graph I "dropped" the cork in three different place (in three colors) and sketched a rought graph of what a solution would look like. All solutions are attracted to the line y=x.
If you drop a cork at (0,0) it will stay on the flow line y=x. This represents the solution to the ODE with inital condition y(0)=0. I hope this helps.How do you interpret that graph? Is that straight line that runs through the origin part of the solution?