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3. For function y(t) with y(0) = 1, y'(0) = -2, y"(0) = 3, y"(0) =...
Find the solution y of the initial value problem 3"(t) = 2 (3(t). y(1) = 0,...
Find the solution y of the initial value problem 3"(t) = 2 (3(t). y(1) = 0, y' (1) = 1. +3 g(t) = M Solve the initial value problem g(t) g” (t) + 50g (+)? = 0, y(0) = 1, y'(0) = 7. g(t) = Σ Use the reduction order method to find a second solution ya to the differential equation ty" + 12ty' +28 y = 0. knowing that the function yı(t) = + 4 is solution to that...
2. for the following differential equation: y + 8y + 15y-u 30u, y(0)-1,y(0) 0,u(t)-t fort20 3....
2. for the following differential equation: y + 8y + 15y-u 30u, y(0)-1,y(0) 0,u(t)-t fort20 3. Find the transfer function
Find y as a function of t if 5y′′+26y=0, y(0)=2,y′(0)=9 y(t) = ?
Find y as a function of t if 5y′′+26y=0, y(0)=2,y′(0)=9 y(t) = ?
(25pt| 3. Find y(t) if x(0) = 0 2 + 2y + u(t), 2.r + y,...
(25pt| 3. Find y(t) if x(0) = 0 2 + 2y + u(t), 2.r + y, y(0) = 2 where it is the unit step function.
(1 point) Find y as a function of t if y-8y = 0, (0) - 6,...
(1 point) Find y as a function of t if y-8y = 0, (0) - 6, (1) = 2. y(t) Remark The initial conditions involve values at two points
х 0<I< 3. The tent function is defined by T(x) = 1 - < x <...
х 0<I< 3. The tent function is defined by T(x) = 1 - < x < 1 2 otherwise (a) Express T(2) in terms of the Heaviside function. (b) Find the Laplace transform of T(x). (c) Solve the differential equation y" – y=T(x), y(0) = y'(0) = 0
(1 point) Find y as a function of t if y" – 107 +9y = 0,...
(1 point) Find y as a function of t if y" – 107 +9y = 0, y(0) = 4, y(1) = 3. y(t) = Remark: The initial conditions involve values at two points.
(1 point) Find y as a function of t if 64y"-81y-0 with O) 3, (0)7.
(1 point) Find y as a function of t if 64y"-81y-0 with O) 3, (0)7.
2y"(t) + 3 y' (t) + y(t)=x"(t) +x'(t) - x(t), y(0) = -2, y'(0) = 0,...
2y"(t) + 3 y' (t) + y(t)=x"(t) +x'(t) - x(t), y(0) = -2, y'(0) = 0, u(t) is the step function. 1. Write an expression for Y(s); at first leave U(s) symbolic. Identify which part is the zero-state and which part is the zero-input frequency-domain solution. Identify which part is the transfer function and which part is the initial condition polynomial. You will need to use the following transform pairs or properties, noting that they apply to the input as...
Consider the bivariate function f(x.y) = (x + y)/3 for 0< x< 1 and 0<y< 2...
Consider the bivariate function f(x.y) = (x + y)/3 for 0< x< 1 and 0<y< 2 and f(x.y) = 0 3. otherwise. (a) Show that f(xy) is a density function. (b) Find the probability that both X and Y are less than one. (c) Find the marginal densities of X and Y and show that they are not independent. (d) Find the conditional density of X given Y when Y = 0.5.
Find the solution y of the initial value problem 3"(t) = 2 (3(t). y(1) = 0, y' (1) = 1. +3 g(t) = M Solve the initial value problem g(t) g” (t) + 50g (+)? = 0, y(0) = 1, y'(0) = 7. g(t) = Σ Use the reduction order method to find a second solution ya to the differential equation ty" + 12ty' +28 y = 0. knowing that the function yı(t) = + 4 is solution to that...
2. for the following differential equation: y + 8y + 15y-u 30u, y(0)-1,y(0) 0,u(t)-t fort20 3. Find the transfer function
(25pt| 3. Find y(t) if x(0) = 0 2 + 2y + u(t), 2.r + y, y(0) = 2 where it is the unit step function.
(1 point) Find y as a function of t if y-8y = 0, (0) - 6, (1) = 2. y(t) Remark The initial conditions involve values at two points
х 0<I< 3. The tent function is defined by T(x) = 1 - < x < 1 2 otherwise (a) Express T(2) in terms of the Heaviside function. (b) Find the Laplace transform of T(x). (c) Solve the differential equation y" – y=T(x), y(0) = y'(0) = 0
(1 point) Find y as a function of t if y" – 107 +9y = 0, y(0) = 4, y(1) = 3. y(t) = Remark: The initial conditions involve values at two points.
(1 point) Find y as a function of t if 64y"-81y-0 with O) 3, (0)7.
2y"(t) + 3 y' (t) + y(t)=x"(t) +x'(t) - x(t), y(0) = -2, y'(0) = 0, u(t) is the step function. 1. Write an expression for Y(s); at first leave U(s) symbolic. Identify which part is the zero-state and which part is the zero-input frequency-domain solution. Identify which part is the transfer function and which part is the initial condition polynomial. You will need to use the following transform pairs or properties, noting that they apply to the input as...
Consider the bivariate function f(x.y) = (x + y)/3 for 0< x< 1 and 0<y< 2 and f(x.y) = 0 3. otherwise. (a) Show that f(xy) is a density function. (b) Find the probability that both X and Y are less than one. (c) Find the marginal densities of X and Y and show that they are not independent. (d) Find the conditional density of X given Y when Y = 0.5.
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