Example 1

Differential Equations

Example 1

Solve:    dy/dx = (x+3x2)/y2      given one point on the line: (0,6).

First separate variables:

   y2 dy = (x + 3x2) dx

Now integrate:

   y3/3 = x2/2 +x3 + C

    Note that we combine the constants into one.

Solve for C, then rearrange to solve for y:

   y = (3x2/2 +3x3 +216) 1/3

   

Example 2