last part will be solved by partial fractions
Solve the following initial value problem For step functions, remember to use u(t- c) rather than...
(1 point) Solve the following initial value problem: y" + 9y = u5(t); y(0) = 0, y' (O) = 0. For step functions, remember to use uſt - c) rather than uc(t). g(t) = ||
(1 point) Use the Laplace transform to solve the following initial value problem: y" +12y' 85y (- 6 (0) 0, y(0)0 Use step(t-C) for ue(t). y(t) = (1/49jeAqt-6))sin(7)step(t-6) (1 point) Use the Laplace transform to solve the following initial value problem: y" +12y' 85y (- 6 (0) 0, y(0)0 Use step(t-C) for ue(t). y(t) = (1/49jeAqt-6))sin(7)step(t-6)
5) Use the method of Laplace transforms to the solve the following boundary value problem IC: u(x, 0) 2 in the following way: a) Apply the Laplace transform in the variable of t to obtain the initial value problem b) Show that U =-+ cie'sz +cge-Vsz s the general solution to the above equation and solve for the constants c and c2 to obtain that c) By taking a power series about the origin and using the identities, sinh iz-...
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...
4. Solve the initial, boundary value problem by the Fourier integral method. u (0,t)0, u(r,t) bounded as-00 4. Solve the initial, boundary value problem by the Fourier integral method. u (0,t)0, u(r,t) bounded as-00
Section 6.5 Impulse Function: Problem 2 Previous ProblemProblem ListNext Problem (1 point) Use the Laplace transform to solve the following initial value problem: y" +4y-96(t-2) y(0-0, y,(0) 0 y(t)- Notation: write u(t-c) for the Heaviside step function ue(t) with step att c.) Preview My Answers Submit Answers Section 6.5 Impulse Function: Problem 2 Previous ProblemProblem ListNext Problem (1 point) Use the Laplace transform to solve the following initial value problem: y" +4y-96(t-2) y(0-0, y,(0) 0 y(t)- Notation: write u(t-c) for...
1. Solve the initial-boundary value problem one = 4 for () <<3, t> 0, u(0,t) = u(3, 1) = 0 for t> 0, u(x,0) = 3x – 2” for 0 < x < 3. (30 pts.)
Solve the initial value problem \(y y^{\prime}+x=\sqrt{x^{2}+y^{2}}\) with \(y(3)=\sqrt{40}\)a. To solve this, we should use the substitution\(\boldsymbol{u}=\)\(u^{\prime}=\)Enter derivatives using prime notation (e.g., you would enter \(y^{\prime}\) for \(\frac{d y}{d x}\) ).b. After the substitution from the previous part, we obtain the following linear differential equation in \(\boldsymbol{x}, \boldsymbol{u}, \boldsymbol{u}^{\prime}\)c. The solution to the original initial value problem is described by the following equation in \(\boldsymbol{x}, \boldsymbol{y}\)Previous Problem List Next (1 point) Solve the initial value problem yy' + -y2 with...
Problem 1: Solve the initial value Dirichlet problem on the half-line and find the value u(1, 2): (8 points) tut(t, z) - trọt, c) = c+t, (t, x) R x [0, +x), u(0, 2) = cos(V), 4(0,2)=e", u(t,0) = 1+ t.
Let u be the solution to the initial boundary value problem for the Heat Equation u(t, x) 4ut, x) te (0, o0), т€ (0, 3)%; with initial condition 2. f(x) u(0, x) 3 0. and with boundary conditions ди(t, 0) — 0, и(t, 3) — 0. Find the solution u using the expansion u(t, a) "(2)"п (?)"а " п-1 with the normalization conditions Vn (0) 1, wn(0) = 1 a. (3/10) Find the functions wn. with index n > 1....