solve the IVP using the Laplace approach
we use partial fraction to findinverse laplace transform.
First we apply laplace transform on both sides of the differential equation then we solve for x(s). For solution x(t) we find inverse laplace transform of x(s).
solve the IVP using the Laplace approach * +0.2 x = cos(4 t), x(0) = 1
Solve the IVP using laplace transformation y”+3y=(t-2)u(t-1) y(0)=-1 y’(0)=2 Solve the IVP usiag laplace transformahbn 3y (t-2) u (t-1) (0) 2 yo)-1 Solve the IVP usiag laplace transformahbn 3y (t-2) u (t-1) (0) 2 yo)-1
solve the IVP using the Laplace approach ï + 2 i + 5 x = e-3t, x(0) = 1, *(0) = 0
use laplace transforms to solve ivp x" + 2x' - 15x = 6delta(t -9), x(0) = -5, x'(0) = 7
Solve each differential equation. (Don't use the Laplace transform. 3. IVP: y + cos(x + y) + (x – y + cos(x + y)) = 0, y(0) = 7. If the equation is exact equation, then solve it. If not, find only an exact equation.
16. Solve the IVP with a Laplace transform method x" + 2x' + 2x = e-t, x(0) = 1, x'(0) = 1
Use the LaPlace Transform to solve the given IVP. y′′ + 4 y= -10e^−t y(=0) 0,−=y′(0) 4
Detailed answer using the Laplace Transforms method Solve the IVP using the method of Laplace transforms AND one other method of your choice. y" +5y' +6y= 2e ; y(0)=1, y'(0) = 3 TABLE 7.2 Properties of Laplace Transforms L{f'}(s) = s£{f}(s) - f(0) L{f"}(s) = s?L{f}(s) – sf(0) – f'(0) . TABLE 71 Brief Table of Laplace Transforms 50 F(x) = ${f}(s) s>0 S 1 => a S a p", n=1,2,... s>0 +1 sin bt s > 0 . s?...
pls do all questions. thanx 1. [5 Consider the IVP rty(t) + 2 sin(t)y(t) = tan(t) y(5)=2 Does a unique solution of the IVP exist? Do not solve the IVP but fully justify you answer. What is the IOE? 2. 4 Consider the ODE Using undetermined coefficients, what is an approprite guess for the coefficient (s) in yp but fully justify you answer. ? Do not solve for 3. [10] Solve the IVP. Use any approach you like y(x) 6y'(x)...
SOLVE #3 AND #4 PLEASE Use the Laplace transformation to solve the IVP. 1. y"-6y' + 9y-24-9t, y(0)-2, y, (0)-0 2. 9y" - 12y'4y50ey(0)--1,y'(0)2 3. У"-2y'--. 1 2 cos(2t) + 4 sin(2t),y(0)-4,y'(0)-0 Use the Laplace transformation to solve the IVP. 1. y"-6y' + 9y-24-9t, y(0)-2, y, (0)-0 2. 9y" - 12y'4y50ey(0)--1,y'(0)2 3. У"-2y'--. 1 2 cos(2t) + 4 sin(2t),y(0)-4,y'(0)-0
Use the Laplace transform to solve the IVP y"(t) + 6y'(t) + 9y(t) = e2t y(0) = 0 y'(0) 1