Solve the initial value problem honhomogeneous equation: LQ"+RQ+ Q = E. coswt initial Conditions: SQ (0)=Qe,...
Differential equation For a 2^nd order DE Lq + Rq + (1/C)q = 0 a) Show that the product of the Eigen values is (1/LC) b) Show that the Sum of the Eigen values is (-R/L) c) Show that if the value of C = L = 1 what must be the maximum R so that we have converging solution? At the maximum value of R, what would be the frequency of driven force to have zero Impedance?
Problem 2. Proof the Initial Value Theorem: lim q(t) = lim sQ(s). E $ 0 Hint: does sQ(s) – q(0) looks familiar to something?
Solve the initial-boundary value problem for the following equation U = N Ux with U(x, 0) = sin (x) +N ,U(0, t) = 0, and U, (N, t) = 0 Q4| (5 Marks) my question please answer Solve the initial-boundary value problem for the following equation U = N Ux with U(x, 0) = sin (x) +N ,U(0, t) = 0, and U, (N, t) = 0 Q4| (5 Marks) Solve the initial-boundary value problem for the following equation Uų...
Section 1.3 3. a. Solve the following initial boundary value problem for the heat equation 0x<L t0 at u(r, 0) f() u(0, t)u(L, t) 0, t>0, 9Tr when f(r)6 sin L b. Solve the following initial boundary value problem for the diffusion equation au D 0 L t0 at u(r, 0) f() (0, t) (L, t) 0, t 0, x < L/2 0. when f(r) r > L/2. 1 Section 1.3 3. a. Solve the following initial boundary value problem...
fx px 3. Solve the following initial value problem (13.2.20): Differential Equation: = (sin t) î - (cost)ġ + (4 sint cost)k Initial Conditions: (0) = î - R op (0) = î
Solve the initial value problem: y''-2y'+y=0, y(0)=2, y'(0)=1 . A) Write its characteristic equation. B) Write a fundamental set of solutions of the homogenous equation. C) Prove that your solutions from B) are independent. D) Find the solution satisfying initial conditions.
and part b solve the initial value problem for the system in (a) with initial position q(0)=a and initial momentum p(0)= wb. a and b are real constant. A ρ。'ntc, p by ferce pro portional to its dis knte fron . If t denotes tre the Punctven) obey s Ne mass m=1 no vesen alae R, at tracted to the origine Where w iss Posit i ue constant ,This ,s know, as the Mumon.lOulleh'F.q order EA. Wrde this Haininic as...
ODE - 1 Q.1 Solve the following first order linear initial value problems. (a) 2ndp - 0.4pdt -0, p(1)- 0.2 (b) v(f) dv (1) +*dt - 0, v(2) -2 + 2v ()- 6, v(0) - 10 (c) (d) The first order differential equation, initial value problem, - Sms, v(0) = 2ms. describes the motion of a car. Find an expression for the speed v () and determine the velocity of the car after 10 seconds from the beginning of its...
4. Consider the following initial value problem: y(0) = e. (a) Solve the IVP using the integrating factor method. (b) What is the largest interval on which its solution is guaranteed to uniquely exist? (c) The equation is also separable. Solve it again as a separable equation. Find the particular solution of this IVP. Does your answer agree with that of part (a)? 5 Find the general solution of the differential equation. Do not solve explicitly for y. 6,/Solve explicitly...
Problem 3. Consider the initial value problem w y sin() 0 Convert the system into a single 3rd order equation and solve resulting initial value problem via Laplace transform method. Express your answer in terms of w,y, z. Problem 4 Solve the above problem by applying Laplace transform to the whole system without transferring it to a single equation. Do you get the same answer as in problem1? (Hint: Denote W(s), Y (s), Z(s) to be Laplace transforms of w(t),...