Solution Found!
st-order DE a curve in the plane defined by f (x, y) = 0
Chapter 2, Problem 17E(choose chapter or problem)
For a first-orde DE dy/dx = f(x, y) a curve in the plane define by f(x, y) = 0 is called a nullcline of the equation, since a lineal element at a point on the curve has zero slope. Use computer software to obtain a direction fiel over a rectangular grid of points for \(d y / d x=x^{2}-2 y\), and then superimpose the graph of the nullcline \(y=\frac{1}{2} x^{2}\) over the direction field. Discuss the behavior of solution curves in regions of the plane defined by \(y=\frac{1}{2} x^{2}\) and by \(y>\frac{1}{2} x^{2}\). Sketch some approximate solution curves. Try to generalize your observations.
Text Transcription:
dy/dx = x^2 - 2y
y=1/2 x^2
y>1/2 x^2
Questions & Answers
QUESTION:
For a first-orde DE dy/dx = f(x, y) a curve in the plane define by f(x, y) = 0 is called a nullcline of the equation, since a lineal element at a point on the curve has zero slope. Use computer software to obtain a direction fiel over a rectangular grid of points for \(d y / d x=x^{2}-2 y\), and then superimpose the graph of the nullcline \(y=\frac{1}{2} x^{2}\) over the direction field. Discuss the behavior of solution curves in regions of the plane defined by \(y=\frac{1}{2} x^{2}\) and by \(y>\frac{1}{2} x^{2}\). Sketch some approximate solution curves. Try to generalize your observations.
Text Transcription:
dy/dx = x^2 - 2y
y=1/2 x^2
y>1/2 x^2
ANSWER:Step 1 of 4
In this problem, we have to show the behavior of the solution curve in the given region defined by 
