![]() ![]() ![]() Check out this complex-plane solution curve for free: Interactivity is available for Wolfram|Alpha Pro users. d^2/ dx^2 f( x, y) + d^2/ dy^2 f( x, y) = 0Ĭalculate solutions to an ODE that are implicit or in terms of special functions:.5 y”” + 4 y”” + 3 y”’ + 2 y” + 1 y‘ + 0 y = 0įind the solution to a general class of differential equations:.Solve a higher-order differential equation: Given a function, we can calculate an ODE such that the given function is a solution: ![]() The coverage of differential equations Wolfram|Alpha provides goes much deeper. For small angles, we can approximate this ODE by y”( t) + y( t) = 0. The solution for this ODE is in terms of special functions, which is not a problem for Wolfram|Alpha. Three methods are provided here for solving this ODE.Īn example of an ODE that models the angle of a pendulum over time is y“( t) + sin( y( t)) = 0. How about we model the position of a spring with resting initial position and velocity, and forcing function sin(2 t): y”( t) + y( t) = sin(2 t), y(0) = 0, y‘(0) = 0. Notice how four methods are provided with the Step-by-step solution. We see Wolfram|Alpha classifies the ODE, solves it, and provides a family of plots. Let’s look at the simple ODE y‘( x) = y( x). Wolfram|Alpha can solve a plethora of ODEs, each using multiple methods. Now, we do not offer ODE-solving primates at the moment, but we can help you with your differential equations problem sets. As the winter term kicks into gear, you might start hoping you had an ODE-solving pet monkey as the math and physics problem sets start piling up. ![]()
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