Solving Differential Equations in R Karline Soetaert, Jeff Cash, Francesca Mazzia
Publisher: Springer

So for the given non-homogeneous equation we need to work with the general solution u(x) = a*e^x + b*e^(-x) + c*sin(x) + d*cos(x). Suleiman, “Implicit r-point block backward differentiation formula for solving first-order stiff ODEs,” Applied Mathematics and Computation, vol. Hopefully you recognize the solution to this equation is $y(t)=e^t$ . A special third-order differential equation (ODE) of the form which is not explicitly dependent on the first derivative and the second derivative of the solution is frequently found in many physical problems such as electromagnetic waves, thin film flow, and gravity driven flows. Without it, the mathematical Indonesia: RUEDC-Press, 2007. Solve differential equation in Calculus & Beyond Homework is being discussed at Physics Forums. It is free and open source, has powerful data processing routines built-in, awesome visualisation tools, and a very large user community that provides even the most exotic analysis methods. To spend more time analyzing data and less programming. Equation m^2 - 1 = 0, and thus m = +/- 1 and so u = a*e^x + b*e^(-x). Although you'd probably also work happily with some other high level language. What's the best programming language to learn for solving partial differential equations? I have a second-order, autonomous, non-linear ODE (well actually when the operator equation is brought into a cylindrical coordinate system it is non-autonomous) and I keep getting an unevaluated expression with "RootOf" in it. Winther, Introduction to Partial Differential Equations: A Computational Approach, New York: Springer-Verlag, 1998. Let's plot that on the same graph. The partial differential equation of heat conduction in tissue medium with the boundary conditions tell us what is happening at the boundaries to affect the solution inside the domain of interest, whereas the initial conditions tell us the state from which the solution evolves. In choosing a high level language, I'd go for R.