Solve the following ODEs. x" + x = cost, x(0) = 0, x"(0) = 0 X" 2x = e x(0) = x'(0) = 0. Hint: Do not try to compute the Laplace trasform of e-42
Solve the following problem u(0, t) 0, u(1,t)-0, t> 0 a(x,0) = f(x), 0 < x < 1 lu (x, 0) = 0, 0
Minimize and Simplify using the Array Technique Code using Verilog 0/0 1/0 1/0 0/0 x/0 0/0 0/0 1/0 x/0 x/0 x/0 0 1 Minimize the number of states 2- Do the state assignments to minimize the IFL and OFL. 3- Complete the design of this state machine using JK flip-flops. 4 Code the state machine. 5- Write a test bench to simulate it. 6- Simulate it for different words. 0/0 1/0 1/0 0/0 x/0 0/0 0/0 1/0 x/0 x/0 x/0...
Let fa(x)= x^a if x>0, 0 if x<0. a) for what values of a is f continuous at 0? WHY is a<0 not continuous at 0? Please explain.
7. x' + 3x + y' = 1 x(0) = 0, y(0) = 0 x' - x + y' - y = et one (am) a) 6 (Psit sy sell JESUS
2d and 4b [2 リ 5 0 -6 200 x(0)=10 x' e2 0 0 |-6-1 3 0 42 0-1-2 x, 43,1 0 0 (d) x' = ' x' (c) x'=12-1-2|x; 2. The matrices in the following systems have complex eigenvalues; use Theorem 2 to find the general (real-valued) solution; if initial conditions are given, find the particular solution satisfying them. 1-x, x(0)-1 (b) x, = (a) x' = X; 0 20 x(0)-|2 이 x, (d) x'=1-20 (c) x' =10-1-6|x; L0...
Let f(x) = 2x4 +x4cos(1/x) for x ̸= 0 and f(0) = 0. Show that 0 is a global minimum x for f but for every neighbourhood V of 0 there exists x,y ∈ V such that f′(x) > 0 and f′(y) < 0.
. Let g(x): 0 if x [0, 1] is rational and g(x) 1/x if x [0, 1] is irrational. Explain why g R[0, 1]. However, show that there exists a sequence (P") of tagged partitions of [a, b] such that |Pl 0 and lim,S(g; P) exists.
0 x/8 x <0 0 11, Find the mean when F(x) = x < 2
Find Fourier series of f(x)= 0 if -35 x<0 and f(x)= 1 if 0 < x <3 which f(x) is defined on [-3,3)