Differential Equations

Example 1

Solve: dy/dx = (x+3x^{2})/y^{2} given one point on the line: (0,6).

First separate variables:

y^{2} dy = (x + 3x^{2}) dx

Now integrate:

y^{3}/3 = x^{2}/2 +x^{3} + C

Note that we combine the constants into one.