question 2 Please show your steps for full or partial credit. Use any Laplace Table to...
Using the Laplace transform, solve the partial differential equation. Please with steps, thanks :) Problem 13: Solving a PDE with the Laplace Transform Using the Laplace transform, solve the equation 山 given the initial and boundary conditions a(x, 0)=1 ifx> 0, u(0, t) -1 if t 2 0. Problem 13: Solving a PDE with the Laplace Transform Using the Laplace transform, solve the equation 山 given the initial and boundary conditions a(x, 0)=1 ifx> 0, u(0, t) -1 if t...
Please help solving all parts to this problem and show steps. (1 point) Use the Laplace transform to solve the following initial value problem: x' = 5x + 3y, y = -2x +36 x(0) = 0, y0) = 0 Let X(s) = L{x(t)}, and Ys) = L{y(t)}. Find the expressions you obtain by taking the Laplace transform of both differential equations and solving for YS) and X (s): X(S) = Y(s) = Find the partial fraction decomposition of X(s) and...
please show all steps (a) Find the Laplace transform of the solution of the initial-value problem y" - 4y + 3y = -3x + 2 cos(3x), y(0) = 2, y (0) = 3. 8² +68 is the Laplace transform of the solution of an intitial-value problem. Find the (8 + 1)(82 +9) solution y = y(a) by finding the inverse transform of Y.
Please show the process used to solve, thanks! Use partial fractions decomposition and the table of Laplace transforms to find the inverse Laplace transform of 8 F(8) $3 +682 +8s
Problem D Solve the following initial value problems using the Laplace Transform. To receive full credit, every time you use LAPLACE TRANSFORM FORMULA indicate which one you used 1. y' – 3y = te3t, y(0) = 1 2. y" – 4y = eat, y(0) = 0, y'(0) = 1 3. y' + y = H(t – 5), y(0) = 2
please explain the steps as well! it’s imp for me to understand this question. i have attached the table for last part of the question Consider the second order non-homogeneous constant coefficient linear ordinary differ- ential equation for y(x) ору , dy where Q(x) is a given function of r For each of the following choices of Q(x) write down the simplest choice for the particular solution yp(x) of the ODE. Your guess for yp(x) will involve some free parameters...
PLEASE SOLVE FULL PROBLEM 2. Derive the time domain representations of the following Laplace transform expressions based on the given ROCs ROC: Refs) > 0, (b) x(s)= 2 , ROC : Re(s) <-1, (c) x(s) = , ROC : 0 < Re(s) < 1, Hint: Try not to use the inverse Laplace transform formula. Expand each expression into partial fractions and determine time domain representations based on the chart and given ROCs
automatic control systems. please show full work and solve neatly. Question 4 Find the Laplace Transform of the following time functions. a) ft)-e+sin(2t-3)+te b) g(t)=2e-3, cos(101-3) Question 4 Find the Laplace Transform of the following time functions. a) ft)-e+sin(2t-3)+te b) g(t)=2e-3, cos(101-3)
Find the following Inverse Laplace transformations. Use the Laplace Transform table attached in the next page. Show all your work, how to get partial fractions etc. and clearly state the Laplace rule(s) that you used in the related step from the attached Laplace Table. (?) ℒ −1 { ? 2−?+2 ?(?−3)(?+2) } (?) ℒ −1 { ? −? ? ? } (?) ℒ −1 { 1 ? 2−2?+1 }. Q1. (15 pts) Find the following Laplace transformations. Use the Laplace...
2. Solve the following partial differential equation using Laplace transform. Express the solution of u in terms of t&x. alu at2 02u c2 2x2 u(x,0) = 0 u(0,t) = f(t) ou = 0 == Ot=0 lim u(x, t) = 0