It may happen that a given ODE is not linear in y(x) but can be viewed as a linear ODE in x(y). In this case, it is said to be an inverse linear ODE. This is an inverse ...

MaxExtraConditions is an option to Solve and related functions that specifies how many extra equational conditions on continuous parameters to allow in solutions that are ...

Two decades of intense R&D at Wolfram Research have given Mathematica by far the world's broadest and deepest coverage of special functions—and greatly expanded the whole ...

The main equations that Solve and related Mathematica functions deal with are polynomial equations. It is easy to solve a linear equation in  x. One can also solve quadratic ...

Here is an example of an exact ODE. This verifies the solution. Here is a contour plot of the solution.

Building on its broad algorithmic and mathematical capabilities, Mathematica provides a unique level of highly general and efficient support for additive number theory.

Do Basic Calculations Do Constrained Nonlinear Optimization Control the Precision and Accuracy of Numerical Results

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 ...

While differential equations have three basic types—ordinary (ODEs), partial (PDEs), or differential-algebraic (DAEs), they can be further described by attributes such as ...

Since many functions in Mathematica give solutions in the form of rules, you need to be able to use these rules to explore and interpret your results. Although many of the ...