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