Initial Value Problem - Unique Solution?

Related BrainMass Solutions

• Differential Equations for Initial condition Changes

  Then the initial-value problem , has a unique solution on the entire interval I. i. Note that the above differential equation and its two initial conditions constitute a second-order initial value problem. ii.

• Initial value problem

  Find three points (a,b) in the plane for which the initial-value problem dy/dx= √(1-y^2 ) y(a) = b has a unique solution,no solution

• Use the Uniqueness Theorem for the Initial Value Problem

  21297 Use the Uniqueness Theorem for the Initial Value Problem 4. For the initial value problem dy/dx = 3y^(2/3), y(2) = 0, (a) does existence uniqueness Theorem 1 imply the existence of a unique solution? Explain.

• Lipschitz Continuity and Initial Value Problems for ODE's

  Then the initial initial value problem (2) y = f (y(t), t), y(t0 ) = y0 , has a unique solution in some interval [t_0 , t_0 + e] for any y_0 ? (a, b) and any t_0 ?

• Non-Linear ODE Systems.

  Solve the Initial Value Problem x' = 3 x^2/3 , x(0) = 0. 2. Show that if we change the IVP to x(0) = 1, the same system , that is x' = 3 x^2/3, still has a unique solution on the interval ( minus infinity, plus infinity).

• Interval of existence of an IVP

  Summary The initial value problem y(xo)=yo has: • a unique solution in an open interval containing xo if xo≠0; • no solution if yo≠0 and xo=0; • infinitely many solutions if (yo,xo)=(0,0) In our problem we conclude that the ODE has a unique solution

• Ordinary Differential Equations and Initial-Value Problems : Unique Solution

  40761 Ordinary Differential Equations and Initial-Value Problems : Unique Solution Find the unique solution satisfying initial conditions y(1)=0 and y'(1)=1 for ty''-(t+2)y'=2y=0, t not equal to 0 Solve t^2y''+3ty'+5y=0 Solve the initial value

• Initial Value Problem

  513012 Initial Value Problem For every xo in R, solve the initial value problem x' = IxI , x(0) = xo and show that the solution is unique on (minus infinity, plus infinity), where f (x) = IxI is the absolute value of x.

• Existence and uniqueness theorem

  For the above initial value problem, the existence and uniqueness theorem states that if p(x), q(x) and f(x) are continuous on some interval (a,b) containing , then there exists a unique solution y(x) to the ode in the whole interval (a,b).