Risultati di ricerca
3 giorni fa · An Euler equation (also known as the Euler-Cauchy equation, or equidimensional equation) is a linear homogeneous ordinary differential equation with variable coefficients of the following form: \[ a_n x^n y^{(n)} + a_{n-1} x^{n-1} y^{(n-1)} + \cdots + a_1 x\, y' + a_0 y = f(x) , \]
5 giorni fa · Write a first-order linear differential equation in standard form. Find an integrating factor and use it to solve a first-order linear differential equation. Solve applied problems involving first-order linear differential equations.
1 giorno fa · With this syntax (first argument equal to "root" or "root2") dae solves the implicit differential equation: g (t,y,ydot) = 0 y (t0) = y0 and ydot (t0) = ydot0. Returns the surface crossing instants and the number of the surface reached in nn. Other arguments and other options are the same as for dae, see the dae help.
4 giorni fa · The general solution to the linear differential equation \( \tau\,\dot{y} + y(t) = f(t) \) can be splitted into the sum \( y(t) = y_h (t) + y_p (t) , \) where y h is the general solution of the associated homogeneous equation \( \tau\,\dot{y} + y(t) = 0 \) that does not depend on the driving (excitation) source, and y p is a ...
2 giorni fa · This section presents the concept of converting a single ordinary differential equation (linear or nonlinear) into an equivalent system of first order differential equations. More precisely, if a single differential equation in normal form is of order n , then it is possible to transfer it to an equivalent system containing n (or ...
2 giorni fa · An illustration of Newton's method. In numerical analysis, Newton's method, also known as the Newton–Raphson method, named after Isaac Newton and Joseph Raphson, is a root-finding algorithm which produces successively better approximations to the roots (or zeroes) of a real -valued function.
5 giorni fa · Solve applications using separation of variables. We now examine a solution technique for finding exact solutions to a class of differential equations known as separable differential equations. These equations are common in a wide variety of disciplines, including physics, chemistry, and engineering.
