Differential Equation Field

Differential Equations(Parameter)

Differential Equation (parameter) can be expressed in the form dx/dt = f(x,y), dy/dt = g(x,y).
The solution of the differential equation are certain functions. The differential equation defines the slope of at the point (x,y) of the certain curve of the function that passes through this point. For each point (x,y), the differential equation defines a line segment with slope (f,g).

Calculus Applets

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Introduction to Differential Equations

Suppose we have an equation like dy/dx = 2x and want to find a solution. Equations with derivatives are called differential equations and solving them means finding a function that satisfies the equation. In this case, y = f (x) = x² + C provides the family of solutions. If we also knew that y = 3 when x = 0, then we'd know that y = x² + 3 is the specific solution. This applet explores solutions to differential equations.

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