For 0 x π , 0S9, π , and 120 , solve the 2-D wave equation subject to the following conditions. u(0,y,t)-0, u(T.yt):0, u(x,0,) u(x,π, t) 0, 0 Boundary condition: C11 1 u(x),0)-sin(x)sin(2y) + sin(2x)sin(4y), 0 at It=0 Initial condition: For 0 x π , 0S9, π , and 120 , solve the 2-D wave equation subject to the following conditions. u(0,y,t)-0, u(T.yt):0, u(x,0,) u(x,π, t) 0, 0 Boundary condition: C11 1 u(x),0)-sin(x)sin(2y) + sin(2x)sin(4y), 0 at It=0 Initial condition:
2. Use eigenfunction expansion to solve the following IBVP: u,(x, t) ="-(x,t) + (t-1)sin(m), 0
3. Solve y" + 2ay' +y -sin(t) with initial condition y(0) -y'(0)0 for all values of a 2 0. Plot the amplitude of oscillations as a function of w for α-1/2 W1 3. Solve y" + 2ay' +y -sin(t) with initial condition y(0) -y'(0)0 for all values of a 2 0. Plot the amplitude of oscillations as a function of w for α-1/2 W1
Solve (D2+2D+2)y=0 Initial Conditions: y(0)=1, y'(0)=2
3. An LTIC system is specified by the equation (D2 9)y(t) (3D 2)x(t) Assume y(0)3,y(0) 6 d) What is the characteristic equation of this system? e) What are the characteristic roots of this system? f Determine the zero-input response yo(t). Simplify your answer 3. An LTIC system is specified by the equation (D2 9)y(t) (3D 2)x(t) Assume y(0)3,y(0) 6 d) What is the characteristic equation of this system? e) What are the characteristic roots of this system? f Determine the...
2. Use separation of variables to solve the IBVP: utt (z, y, t) u(0, y, t) u (x, y,0) uzz(z, y, t) + un, (x, y, t) = 0, 0 < x < 1, 0 < y < 1, 0, u(1,y,t)=0, u(z,0,t)=0, u(z, l,t) = 0 sin(r) sin (2my), ue (r, y,02 sin(2mx) sin(ry) t > 0, = =
Use the Laplace transform to solve the given initial-value problem.y'' + y = 2 sin(2t), y(0) = 11, y'(0) = 0y(t) =
Use the Laplace transform to solve the given initial-value problem.y'' + y = 2 sin(2t), y(0) = 11, y'(0) = 0y(t) =
Solve the following ODE for y(x) y''+y'-2y=sin(2x) y(0)=2 y'(0)=0
7c. Solve for x and y by using unimodular row reduction with initial parameters x=0 and y=1 when independent variable t=0 2x(D-2) + 6y = 0 2x + y(D-1) = 0