Find the general solution of the differential equation: y' - 2y = e-³t Use lower case c for the constant in your answer.
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- x = c1 cos t c2 sin t is a two-parameter family of solutions of the second-order de x'' x = 0. find a solution of the second-order ivp consisting of this differential equation and the given initial conditions. x(π/4) =√2 , x'(π/4) =2√2Consider nonnegative integer solutions of the equation x1+x2+x3+x4+x5+x6=30. How many different solutions are there? How many solutions also satisfy: for every i∈{1,2,3,4,5,6}, xi is positive and even?Show that F(x, y, z) = xy + xz + yz has the value 1 if and only if at least two of the variables x, y, and z havethe value 1.
- Prove that there are no solutions in positive integers x and y to the equation ?3 + ?3 = 125 (Hint: Use proof by cases and, if useful, WLOG.)Write computer codes using any programming language for one of the following methods to solve a linear equation system.1- Gaussian elimination.2- LU decomposition.3- Gauss-Seidel iterations.Execute the program for the linear equation system given below.Which option is correct for the following system equation? x-y-z=4 2x-2y-2z=8 5x - 5y - 5z = 20 answer a)Finite solutions b)No solution c)Subzero solutions d)Infinitely many solutions e)Unique solution
- programming solve for the value of xFind the values, if any, of the Boolean variable x that satisfy these equations. a) x · 1 = 0 b) x + x = 0c) x · 1 = x d) x · ??̅ = 1Two trigonometric identities are given by: (sin x + cos x)2 = 1+ 2 sin x cos x 1- 2 cos x - 3cos2 x = 1- 3cos x sin2 x 1- cos x For each part, verify that the identity is correct by calculating the values of the left and right sides of the equation using MATLAT, substituting x=200 Find the solution to the systems + = ... .. . y + 3 y + 2 y y u Where y (0) =0; y’ (0) =0. u (t) is a square wave.
- Given A = {1,2,3} and B={u,v}, determine. a. A X B b. B X BResearch at least two (2) other methods of solving simultaneous equation with three (3) variables aside from Cramer’s Rule and substitution method as solution.Let E : y2 = x3 + 3x + 4 be an elliptic curve over F37. (a) Find all the elements of the elliptice curve group.(b) Find the order of the group.(c) Find a primitive element of this group and call it G.(d) Compute [30]G = G ⊕ G ⊕ · · · ⊕ G (addition of 30 many G’s) kindly help with full explanation. Thank you!