Linearity is an important concept to be familiar with. For the following operators, L.), determine if...
Determine the order and linearity of the differential equation: I do 3 (Copy) + y = 0. dx ) (A) First order and linear (B) Third order and linear (C) Fourth order and linear (D) First order and nonlinear (E) Third order and nonlinear (F) Fourth order and nonlinear
Classification of ODEs Determine the order and linearity/nonlinearity of the following scalar ODEs (a) (10 points) y"(t) sin(t) y(t) +t2 (b) (10 points) y'(t)-sin(y(t))- t Note: If the equation is linear, vou need to prove it by the linearity property. If the equation is nonlinear, only determine the term in the equation that makes it nonlinear S. S.
A probability density function f(x) is an important concept in statistical sciences. It gives you the distribution of the random variable x. f(x) usually defined in a certain interval, and vanish in the rest. One can defined the median u and variances o2 as using the probability density function as (you'll see more about this later on in the course of statistic): u=L" xf(x)dx 2= (x – u)? dx For most cases the distribution function is normal or Gaussian. If...
Which of the following functions has the same end behavior as f'(x) = ax3 + bx? + cx + d? Oaxi - bx3 + cx? + dx + e -ax -ax2 + bx + c ax + b
What are the results of operating on the following functions with the operators d/dx and d2/dx2 : a) 4x-3 b) cos(bx), c) eikx d) (x2–i) ? What functions are eigenfunctions of these operators? What are the corresponding eigenvalues?
(1 point) Which of the following operators in R are linear? |(10,9,8)7 A. L(x) В. L(x) — (4г, — 622 + 523, 21, — 10хз, — 821 — 9г2)Т |C. L(x) (x2, x3, H1)7 D. L(x) E. L(x) (812, —З/3, — 7г,)T (5a1, 61, 3r1T
7. Determine the radius of convergence and the interval of convergence for the power series: (-1)"+1" n2 nxn b. An=1 > C. X- + 3! 5! 8. A probability density function f(x) is an important concept in statistical sciences. It gives you the distribution of the random variable x. f(x) usually defined in a certain interval, and vanish in the rest. One can defined the median j and variances oas using the probability density function as (you'll see more about...
Determine the appropriate form of the particular solution for
the following non-homogeneous linear differential equation with
constant coefficients.
J.(4) +9y" = 5 + e' (x – 3) + 4sin(3x). Ax + B + C sin(3x) + D cos(3x) + Exer Ax? + Bxe - 3x + Cxe3x + Det + Exet A + Bxe-3x + Cxe3x + Det + Exet none of these A+B sin(3x) + Cx sin(3x) + Det + Exel Ax2 + Bx cos (3x) + Cxsin (3x)...
5. Determine the convergence of the series: 1 V11 - 4 V11 + 4 V13-4 1 1 1 + 1 13+ 4 + 1 15 + 4 +.. 15-4 6. A rod with length L is lying in the x-axis, with one of its edge is located at the origin. According to the Newton's law of gravity, if the density of the rod is 1 and Newton's constant is then the gravitational field at the point C = (A, B)...
#10 all parts
In each of Problems 5 through 18: (a) Determine all critical points of the given system of equations. (b) Find the corresponding linear system near each critical point. (c) Find the eigenvalues of each linear system. What conclusions can you then draw about the nonlinear system? (d) Draw a phase portrait of the nonlinear system to confirm your conclusions or to extend them in those cases where the linear system does not provide definite information about the...