If the given second-order ODE is inhomogeneous, DSolve applies the method of variation of parameters to return a solution for the problem. This solves an inhomogeneous linear ...

N[expr] gives the numerical value of expr. N[expr, n] attempts to give a result with n-digit precision.

BooleanConvert[expr] converts the Boolean expression expr to disjunctive normal form.BooleanConvert[expr, form] converts the Boolean expression expr to the specified ...

DSolve[eqn, y, x] solves a differential equation for the function y, with independent variable x. DSolve[{eqn_1, eqn_2, ...}, {y_1, y_2, ...}, x] solves a list of ...

The Lotka–Volterra system arises in mathematical biology and models the growth of animal species. Consider two species where Y_1(T) denotes the number of predators and Y_2(T) ...

If you represent the n^th term in a sequence as a[n], you can use a recurrence equation to specify how it is related to other terms in the sequence. RSolve takes recurrence ...

Mathematica uses the Microsoft math recognizer that is built into Windows 7 to recognize handwritten mathematical expressions. This allows you to enter handwritten ...

Many real-world applications require the solution of IVPs and BVPs for nonlinear ODEs. For example, consider the logistic equation, which occurs in population dynamics. This ...

Here is a system of two ODEs whose coefficient matrix has real and distinct eigenvalues. This solves the system. Note that the general solution depends on two arbitrary ...

MakeBoxes[expr, form] is the low-level function used in Mathematica sessions to convert expressions into boxes. MakeBoxes[expr] is the function to convert expr to ...