$Differential Equations$

Differential Equations

Solve the main types of differential equations and initial value problems numerically.

Equation type:

Separable: y′ = f(x) · g(y), the field below is f(x)

First-order linear: y′ + p(x)·y = q(x), the field below is p(x)

Second order: a y″ + b y′ + c y = k, the field below is a

Initial value problem y′ = F(x, y) numerically, the field below is F(x, y)

Expression:

g(y) =

Modes 1–3 are solved exactly. In mode 3 the initial values y(0) and y′(0) are required. Mode 4 is numerical. The calculator does not recognise other types of equations.

This calculator solves the main types of differential equations: separable, first-order linear and second-order linear with constant coefficients. For any y′ = F(x, y) it solves the initial value problem numerically.

Example. y′ = 2xy gives ln|y| = x² + C. y″ − 3y′ + 2y = 0 with y(0) = 0, y′(0) = 1 gives y = eˣ·(eˣ − 1).

Other types of equations are not recognised. A numerical answer is marked as approximate.