AS/A2 Pure 5 Pure 6

P4 Topic 5: First Order Differential Equations
Families of solutions 2
When solving the differential equation dy/dx = y, the solution will have an arbitary constant, c. There is therefore a family of solutions that depend on the value of c. In the following display a family of solution curves is shown. You can display any particular solution by changing the value of c. For this curve, the fact that dy/dx = y is illustrated by the green tangent line.

Summary The differential equation dy/dx = y has the solution y = ex+c. Based on free Java applets from JavaMath