please 3. Solve come to 4. Solve C[f(t)) Where f(t) = 2t Osts 1 f(t) =...
3. Find the Laplace transform off, where f(t) = 3 + 2 if Ost <3, f(t) = 0 if 3 st < 6 and f is periodic with period 6. 4. Solve y" - 16y = 40e4t y(0) = 5, y(0) = 9 using the Laplace transform.
Problem 4. Solve for the functions u, v, and w, where (1) (∂/∂t + ∂/∂x) u = a, (2) (∂/∂t − ∂/∂x) v = b, and (3) (∂/∂t + 3 ∂/∂x) w = c, where a, b, and c are the functions that you calculated in Problem 3... a=f(x+t)= (x+t)^2+(x+t)+1 b=f(x-2t)= (x-2t)^2+(x-2t)+1 c=f(x-3t)= (x-3t)^2+(x-3t)+1
The nonnegative function given below is a probability density function. e-2t/3 if t 20 0 if t < 0 (a) Find P(Osts 3). (b) Find E(t).
8. (i) Find C[F(t)], where F(t) = { if 0 st 34, ift> 4 (ii) Compute the convolution e2 et directly by the definition of the convolution (iii) Evaluate Lle-2445 - e cos(4t) + sin(V2t)). blom.
please show all steps Find L{f}(s) directly by evaluating the integral if 2t when 0 <t<3, when t > 3.
Find f. f'(t) = 2t - 4 sint, (0)= 5 Select one: a. f(t) = 2t - 3 sint +5 O b. f(t)= +2 +4 cost +1 c. f(t)=12 - 3 cost-5 d. f(t) = x2 +3 cost e. None of these
An electromotive force _S210, Osts 50 10, t> 50 is applied to an LR-series circuit in which the inductance is 30 henries and the resistance is 3 ohms. Find the current i(t) if i(0) = 0. ,osts 50 i(t) = t> 50
Problem 3: Insights into Differential Equations a. Consider the differential equation 습 +4 = f(t), where f(t) = e-u, 12 0. Please write the forms of the natural and forced solution for this differential equation. You DO NOT need to solve. (7 points) b. Again consider the differential equation f(t), where f(t) is an input and y(t) is the output (response) of interest. Please write the differential equation in state-space form. (10 points) c. The classical method for solving differential...
2t +1 if 0 <t< 2 Consider f(t) = { | 3t if t > 2. (a) Use the table of Laplace transforms directly to find the Laplace transform of f. (b) Express f in terms of the unit step function, then use Theorem 6.3.1 to find the Laplace transform of f.
Solve the equation. 3 2t + 2 4 5 (Type t = an integer or a simplified fraction.) Solve the equation. 3 2t + 2 4 5 (Type t = an integer or a simplified fraction.)