For the equation

the independent variable is and the dependent variable is . The solution to this equation can be found by simply integrating both sides to give

This form of the solution, where the value of the constant (or constants, for higher order equations) is not known is called the general solution. The solution whose curve passes through the points , say, is called the particular solution, where the value of the constant is known. Given the point, the value of the constant can be found by substituting the coordinates of the point into the equation and solving it to find the constant.

As an example, consider the equation . To solve it, we integrate both sides to give . If this curve passes through the point , we can deduce the value of the constant by substituting into the equation as follows.

This gives