## Differential Equations

We well know how to find the gradient function of a curve,We just differentiate the function we have forWe also need to be able to find y if we are givenTo do this we have to integrate. When we integrate we obtain a function ofbut the function we obtain is not fixed until we have a point on the curve. This is because if we differentiate y to findthen any constant term, for exampledisappears. Hence when we integrate, we add an arbitrary constant. We find the value of this constant by substituting a point on the curve into the equation.

Example:whenFind y as a function of