AS/A2 Pure 5 Pure 6

P4 Topic 5: First Order Differential Equations
Families of solutions 1
The solution to the differential equation dy/dx = mx is y = 0.5mx2 + c, and has an arbitary constant, c. There is therefore a family of solutions that depend on the value of c. In the following displays families of solutions curves are show. You can display any particular solution by changing the value of c. dy/dx = mx is illustrated by the green line.

Summary The differential equation dy/dx = mx has the solution y = 0.5mx2 + c. Based on free Java applets from JavaMath