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Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically.

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Sketch a few solutions of the differential equation on the slope field and then find the general solution analytically. To print an enlarged copy of the graph, go to the website www. mathgraphs . com.

asked Feb 16, 2015 in CALCULUS by anonymous

1 Answer

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Step 1:

The differential equation is image.

Slope field is image.

A direction field is graphical representation of the solutions of a first order differential equation.

Create a table to compute the slope at several values of and .

Now draw the short line segments with their slopes at respective points.

The result is the slope field of the differential equation.

Now draw a solution curve so that it move parallel to the near by segments.

In the similar manner, draw few more solutions of the differential equation.

Graph the slope filed of differential equation and their solutions:

image

Note : The curve in pink color are the solution curves.

Step 2:

Consider image.

Re-write the equation.

image

Integrate on each side.

image

Take exponents of each side.

image

Properties of natural logarithms: image.

image

The solution of the differential equation is image.

Solutions:

Graph the slope filed of differential equation and their solutions is

image

The solution of the differential equation is image.

answered Feb 18, 2015 by Lucy Mentor

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