Examples of Equations That Can Be Made Separable

Examples--Equations That Can Be Made Separable

Example 6: Homogeneous Example

The pictures below show solutions to the equation at the right for values of y₁(-3 red, -1 green, 1 blue, 2 orange, 3 purple). Click on the picture to see an animation of the solutions as y₁ goes from -3 to 3. Quicktime Version

Solution Graph with Slope Field for y(1) = 1

The purple and orange solution graphs would also not be meaningful to the right of their vertical asymptotes. Investigate solutions to this problem using the First Order DE Solution Grapher.

Section 2.5 #6 (Link to another worked out example)

Example 13: Here is another example of an equation that is not separable but can be made separable using an appropriate substitution.

Example 2.5 Number 24 above with y(0) = 1

DPGraph picture of z = (x+y)² - 2x and z = c

The initial value for c is 1. You can use the scrolbar to change the value of c.

Example 14: Another Homogeneous Equation (2.5 #14)

This one is not so easy to graph even by point plotting but you could approximate the graph of the solution by looking at

and using the First Order DE Solution Grapher.
We can also look at this DPGraph Picture of the solution. The view is from the top with z between -0.0001 and +0.0001 so you have the effect of looking at the graph of
or we can look at this DPGraph Picture of the graph of
and look at the z-slice corresponding to z = 0. You could just use Maple.

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Lane Vosbury, Mathematics, Seminole State College email: vosburyl@seminolestate.edu