consider the variation of constants formula
where P(t)=
a) show that solves the initial value problem
x'+p(t)=(t)
x()=
when p and q are continuous functions of t on an interval I and
consider the variation of constants formula where P(t)= a) show that solves the initial value problem x'+p(t)=(t) x()= when p and q are continuous functions of t on an interval I and tg p(s)d...
(A) Find the largest x-interval where the initial value problem has a unique solution: Where A, B, C, D, E, F are some known constants. (B) Determine whether the set of functions could form a fundamental set of solution of a linear differential equation Thank you We were unable to transcribe this image5, sinx, cos2.c
find the solution of the inhomogeneous system for y" +p(t)y' +q(t)y = f(t), a second order scalar equation with p, q, f continuous on interval I, for which (to ) = 0, to on I We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Q. Determine whether the given functions are exponentially bounded and piecewise continuous on 0 ≤ t < ∞. (a) f(t) = tant (b) f(t) = cosh2t (c) f(t) = , where denotes the greatest integer less than or equal to t. We were unable to transcribe this imageWe were unable to transcribe this image
a) By direct substitution determine which of the following functions satisfy the wave equation. 1. g(x, t) = Acos(kx − t) where A, k, are positive constants. 2. h(x, t) = Ae where A, k, are positive constants. 3. p(x, t) = Asinh(kx − t) where A, k, are positive constants. 4. q(x, t) = Ae where A, a, are positive constants. 5. An arbitrary function: f(x, t) = f(kx−t) where k and are positive constants. (Hint: Be careful with...
how do I take the laplace transform of this? I'm trying to find X(s). . I already found a solution but I want to verify if it's correct. The unit inside f0 is 1(t). they're step functions. I forgot to add though The initial conditions are x(0)=0 and . We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
7. Consider these two boundary-value problems: r"-f (t, x, x') 1. Show that if x is a solution of boundary-value problem ii, then the function yt) x((t -a)/h) solves boundary-value problem i, where h b-a 7. Consider these two boundary-value problems: r"-f (t, x, x') 1. Show that if x is a solution of boundary-value problem ii, then the function yt) x((t -a)/h) solves boundary-value problem i, where h b-a
Consider the following statements. (i) Given a second-order linear ODE, the method of variation of parameters gives a particular solution in terms of an integral provided y1 and y2 can be found. (ii) The Laplace Transform is an integral transform that turns the problem of solving constant coefficient ODEs into an algebraic problem. This transform is particularly useful when it comes to studying problems arising in applications where the forcing function in the ODE is piece-wise continuous but not necessarily...
Find the value of x(t) at a given value of t, with initial conditions of x(0) and (0), using Euler Method. Consider the following dynamic system 1 (0 (t) wheere 0.5, xt20 に 4, and m 4 k- We were unable to transcribe this image Consider the following dynamic system 1 (0 (t) wheere 0.5, xt20 に 4, and m 4 k-
QUES 2!!! Problem 1: For the feedback system shown below, compute the transfer functions e/d, x/r. What are the steady-state values for a constant d,r and when do they approach 0 asymptotically as t goes to infinity? C(s) 一心 - P(s) We were unable to transcribe this image Problem 1: For the feedback system shown below, compute the transfer functions e/d, x/r. What are the steady-state values for a constant d,r and when do they approach 0 asymptotically as t...
1 Let f (t), g(t) be a continuous function on some interval I, and to e I. Prove that the initial value problem y'(t) f(t)y + g(t)y2, y(to) zo has a unique and continuous solution φ(t) on a small interval containing to, φ(t) satisfies the initial condition φ(to) = to. 1 Let f (t), g(t) be a continuous function on some interval I, and to e I. Prove that the initial value problem y'(t) f(t)y + g(t)y2, y(to) zo has...