![]() ![]() ![]() X t = &ExponentialE − t, y t = − &ExponentialE − t + &ExponentialE −1įor detailed information on the dsolve command, see dsolve/details. Solve the system of ODEs subject to the initial conditions ics. X t = c_2 &ExponentialE − t, y t = − c_2 &ExponentialE − t + c_1 ![]() If the unknowns are not specified, all differentiated indeterminate functions in the system are treated as the unknowns of the problem. Sys_ode ≔ &DifferentialD &DifferentialD t y t = x t, &DifferentialD &DifferentialD t x t = − x t Sys_ode ≔ &DifferentialD &DifferentialD t y t = x t, &DifferentialD &DifferentialD t x t = − x t Odetest series_sol, ode, ics, series Series_sol ≔ dsolve ode, ics, y x, series Test whether the ODE solution satisfies the ODE and the initial conditions (see odetest ).įind a series solution for the same problem. You can use NDSolve to solve systems of coupled differential equations as long as each variable has the appropriate number of conditions. Sol ≔ dsolve ode, ics, y x, method = laplace Y x = 3 &ExponentialE 2 x 4 + 3 &ExponentialE − 2 x 4 − 1 2Ĭompute the solution using the Laplace transform method. Solve ode subject to the initial conditions ics. Y x = &ExponentialE 2 x c_2 + &ExponentialE − 2 x c_1 − 1 2 Ode ≔ &DifferentialD 2 &DifferentialD x 2 y x = 2 y x + 1 Ode ≔ &DifferentialD 2 &DifferentialD x 2 y x = 2 y x + 1 To define a derivative, use the diff command or one of the notations explained in Derivative Notation. Coupled non-linear differential equations. For more information, see dsolve and worksheet/interactive/dsolve. Using the assistant, you can compute numeric and exact solutions and plot the solutions. The ODE Analyzer Assistant is a point-and-click interface to the ODE solver routines. Computing numerical (see dsolve/numeric ) or series solutions (see dsolve/series ) for ODEs or systems of ODEs. Computing solutions using integral transforms (Laplace and Fourier). Computing formal solution for a linear ODE with polynomial coefficients. Computing formal power series solutions for a linear ODE with polynomial coefficients. Solving ODEs or a system of them with given initial conditions (boundary value problems). Computing closed form solutions for a single ODE (see dsolve/ODE ) or a system of ODEs, possibly including anti-commutative variables (see dsolve/system ). At first I tried to solve it using just the BVPs but Mathematica couldnt do it, so I started using shooting method and turning it into an IVP. (See the Examples section.)Īs a general ODE solver, dsolve handles different types of ODE problems. Im trying to solve these two coupled 2nd order differential equations: with the following boundary conditions. (optional) depends on the type of ODE problem and method used, for example, series or method=laplace. , where are constants with respect to the independent variable Initial conditions of the form y(a)=b, D(y)(c)=d. Ordinary differential equation, or a set or list of ODEsĪny indeterminate function of one variable, or a set or list of them, representing the unknowns of the ODE problem ![]() Note that I have made no attempt to choose reasonable constraints and boundary conditions I have just chosen numbers that would give a solution, to give you a jump start on the syntax.Solve ordinary differential equations (ODEs) Here is an example to show you how you might be able to set this up. A human reader might be able to infer that from context, but a computer system has to have it all spelled out unequivocally. Syntactically, NDSolve was complaining about the fact that you had not specified the independent variable for the $u$ and $v$ functions each time. There were syntactic and conceptual problems with your formulation.Ĭonceptually, NDSolve is a numerical solver, so you need to specify boundary conditions as well as a numerical range of integration for the independent variable, which were missing in your formulation. ![]()
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