Solving cubic first-order ODEs - Mathematics Stack Exchange
WEBJul 3, 2022 — u du dξ + a1(ξ)u = a3(ξ) − a2(ξ)ξ u du dξ + a1(ξ)u = a4(ξ) This is a nonlinear first order ODE to be solved for u(ξ). Supposing that one can solve it the problem is far to be fully solved. One will have to integrate η = ∫ dξ u (ξ) and finally invert η(ξ) for ξ(η). Thanks a …
Find the explicit solution of the ODE - Mathematics Stack Exchange
WEBOct 8, 2020 — 1. How to find the explicit solution for this ode. z ″ − 2z3 + 3z2 − z = 0. Suppose lims → ∞z = 1, lims → − ∞z = 0, lims → ∞z ′ = 0. This is actually from Evans'PDE Chapter 4.5. I obtain this ode from the given condition. But the question asks to solve this explicitly. The method in the textbook is phase plane analysis ...
Solving ODE with initial condition - Mathematics Stack Exchange
WEBSep 28, 2016 — 1. Solve differential equation dx dt d x d t = x(1 − x) cos(x) x (1 − x) cos (x) with x(t) x (t) being the solution of the ODE and x(0) = 1 2 x (0) = 1 2 and find limit t → ∞ t → ∞ of x(t) x (t). I'm having trouble integrating the equation. I did rewrite the equation to.
ordinary differential equations - How to solve the ODE using …
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Solving an initial value ODE problem using Fourier transform
WEBI don't understand why "α=β=0", i.e. why there should not be the general solution of the homogeneous equation in the solution? (2) I don't see how the initial conditions are used in the method by Fourier transform. Does the method by Fourier transform solve an ODE with or without its initial conditions? $\endgroup$ –
Particular solution of second order differential equation
WEBDec 2, 2018 — 1. Both your attempts are in fact right but fail because the fundamental set of solutions for your second order ODE is given by exactly your both guesses for the particular solution. It is not hard to show by using the characteristic equation that the fundamental set of solutions is given by. y(t) = c1et + c2tet.
Which numerical method to use for ODE? - Mathematics Stack …
WEBIn the implicit equation, instead of solving it directly via Newton's method, you can "guess" values with an explicit method (like Runge-Kutta) and then use those guesses in the implicit equation. These are predictor-corrector methods which don't have as much stability as the implicit methods, but have more than the Runge-Kutta methods and are ...
General Solution of a Differential Equation using Green's Function
WEBFirst we seek a solution of the form y = u1(x)y1(x) + u2(x)y2(x) where the ui(x) functions are to be determined. We will need the first and second derivatives of this expression in order to solve the differential equation. Thus, y ′ = u1y ′ 1 + u2y ′ 2 + u ′ 1y1 + u ′ 2y2 Before calculating y ″, the authors suggest to set u ′ 1y1 ...
Solving system of linear differential equations by eigenvalues
WEBSolving linear system of differential equations of 2nd order. 1. Solution of system of linearly dependent ...
ordinary differential equations - Solving an ODE with a Power …
WEBApr 26, 2017 — Addition: Since the ODE is linear one can solve the two cases (y0,v0) = (1, 0) (y 0, v 0) = (1, 0) and (y0,v0) = (0, 1) (y 0, v 0) = (0, 1) as any other solution is a linear combination of these. Now that you have fixed values for a0 a 0 and a1 a 1 it's easy to write a program to canculate hundreds of coefficients - if thats your thing ;o)