AS/A2 Pure 5 Pure 6

P4 Topic 5: First Order Differential Equations
Families of solutions 3
The solution of the differential equation dy/dx = f(x) will be y = F(x) + c, where F(x) is the integral of f(x) The solution 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 solution curves are shown. You can display any particular solution by clicking at any point on the graph. The x-coordinate of the point you click determines c. [Ignore the first input box.]

Summary Clearly the differential equations given above have these solutions: dy/dx y 2x x2 + c 3x2 x3+ c cos x sin x + c 1/x ln x + c ex ex + c Note that the x value you click on is not the value of c itself. It determines where the solution y is zero. Based on free Java applets from JavaMath