5) Use the method of Laplace transforms to the solve the following boundary value problem IC: u(x...
6. Solve an ODE Using Laplace Transforms: For this problem you are to use Laplace Transforms. Find the complete solution for the initial value problem yº+w2y = t +u.(t - Ttcost, y(0) = 1, y(0) = 0. Hint: Look carefully at the second forcing term and rewrite cost. You can solve this by brute force using the integral below. It would be a good exercise to make sure both approaches give the same Laplace transform. The integral The solution ſeat...
Solve the given initial value problem using the method of Laplace transforms. y'' + 3y' +2y = tu(t-3); y(0) = 0, y'(0) = 1 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms. Solve the given initial value problem. y(t) = | Properties of Laplace Transforms L{f+g} = £{f} + L{g} L{cf} = CL{f} for any constant £{e atf(t)} (s) = L{f}(s-a) L{f'}(s) = sL{f}(s) – f(0) L{f''}(s) =...
7.6.27 Solve the given initial value problem using the method of Laplace transforms. z"' + 6z' + 8z = e-bu(t-1); Z(0) = 2, z'(0) = -6 Click here to view the table of Laplace transforms. Click here to view the table of properties of Laplace transforms Solve the given initial value problem. z(t)=
help #7. Solve the initial value problem using the method of Laplace transforms. y""+y" + 3y' - 5y = 16e- yO=0 v'O)=2 y"(= - 4 Before you start solving for y(s), write your Laplace transform of the equation on your Answer Sheet. If you obtain a solution, add it to your Answer Sheet later. [Hint: if you are having trouble factoring a polynomial of high degree, check on simple roots like -1 or 1.]
Use Fourier transforms to solve the boundary van ns to solve the boundary value problem Uzr +tyy = 0, 3ERy>, u(7,0) = 2,7 32; (,0) = 0, < > 2, u is bounded
Show work please (1 point) Use Laplace transforms to solve the integral equation y(t) – v yết – U) do = 4. The first step is to apply the Laplace transform and solve for Y(s) = L(y(t)) Y(s) = Next apply the inverse Laplace transform to obtain y(t) y(t) =
Use Laplace transforms to solve the following initial value problem. x" + x = sin 8t, x(0) = 0, x'(0) = 0 Click the icon to view the table of Laplace transforms. The solution is x(t) = (Type an expression using t as the variable. Type an exact answer.)
Use Laplace transforms to solve the following initial value problem. X' + 2y' + x = 0, x'- y' + y = 0, x(0) = 0, y(0) = 400 Click the icon to view the table of Laplace transforms. The particular solution is x(t) = and y(t) = (Type an expression using t as the variable. Type an exact answer, using radicals as need
Problem 7. PREVIEW ONLY -- ANSWERS NOT RECORDED (20 points) Use Laplace transforms to solve the integral equation y(t) – 16 't – v)y(m) dv = 16t. JO The first step is to apply the Laplace transform and solve for Y(s) = L(y(t)) Y(s) Next apply the inverse Laplace transform to obtain y(t) g(t)
(1 point) Use the Laplace transform to solve the following initial value problem x, = 10x + 4y, y=-6x + e4, x(0) = 0, y(0) = 0 Let x(s) L {x(t)) , and Y(s) = L {y(t)) Find the expressions you obtain by taking the Laplace transform of both differential equations and solving for Y(s) and X(s): S)E Y(s) = Find the partial fraction decomposition of X(s) and Y(s) and their inverse Laplace transforms to find the solution of the...