Solution Found!
Figure 7-4g shows the slope field for the differential equation Figure 7-4gUse a copy of
Chapter 7, Problem 1(choose chapter or problem)
Figure 7-4g shows the slope field for the differential equation
\(\frac{d y}{d x}=\frac{x}{2 y}\)
Use a copy of this figure to answer these questions.
a. Show that you understand the meaning of slope field by first calculating dy/dx at the points (3, 5) and (-5, 1) and then showing that the results agree with the figure.
b. Sketch the graph of the particular solution of the differential equation that contains the point (1, 2). Draw on both sides of the y-axis. What geometric figure does the graph seem to be?
c. Sketch the graph of the particular solution that contains the point (5, 1). Draw on both sides of the x-axis.
d. Solve the differential equation algebraically. Find the particular solution that contains the point (5, 1). How well does your graphical solution from part b agree with the algebraic solution?
Questions & Answers
QUESTION:
Figure 7-4g shows the slope field for the differential equation
\(\frac{d y}{d x}=\frac{x}{2 y}\)
Use a copy of this figure to answer these questions.
a. Show that you understand the meaning of slope field by first calculating dy/dx at the points (3, 5) and (-5, 1) and then showing that the results agree with the figure.
b. Sketch the graph of the particular solution of the differential equation that contains the point (1, 2). Draw on both sides of the y-axis. What geometric figure does the graph seem to be?
c. Sketch the graph of the particular solution that contains the point (5, 1). Draw on both sides of the x-axis.
d. Solve the differential equation algebraically. Find the particular solution that contains the point (5, 1). How well does your graphical solution from part b agree with the algebraic solution?
ANSWER:Step 1 of 5
We will consider each part separately and solve it. Since the image given in the textbook is of poor resolution, we have drawn our own slope field using an online field plotter.
