3' (20 pts) It is known that three solutions to some linear ODE system у,-Ag are...
You are told that a certain second order, linear, constant
coefficient, homogeneous ode has the solutions
y1(x) = e^γx cos ωx, and y2(x) = e^γx sin ωx,
where γ and ω are real-valued parameters and −∞ < x <
∞.
4. You are told that a certain second order, linear, constant coefficient, homogeneous ODE has the solutions where γ and w are real-valued parameters and-oo < x < oo. (a) Compute the Wronskian for this set of solutions. (b) Using...
my solutions say linearly independent but i dont understand
why
4. (5 pts) Let zu(e) = (2-1), sz(t) = [et] Determine whether the vector functions are linearly dependent or linearly independent on (-0,00). ww/xix.7(4) = fet to +-+-0 W[X, Xz] (t) = 0
Given a second order linear homogeneous differential equation а2(х)у" + а (х)У + аo(х)у — 0 we know that a fundamental set for this ODE consists of a pair linearly independent solutions yı, V2. But there are times when only one function, call it y, is available and we would like to find a second linearly independent solution. We can find y2 using the method of reduction of order. First, under the necessary assumption the a2(x) F 0 we rewrite...
21 13 pts) 2. Find a basis for the solution space x of the following linear homogeneous system of equations: 1+2 +3 +14 213r2+4r3- 5x4 4x1+6r2 +8T3- 10x4 6r1 +9r2 +12r3 - 15r4= 0 0 Your solution must include verification that the basis spans the set of all solutions and is linearly independent.
21 13 pts) 2. Find a basis for the solution space x of the following linear homogeneous system of equations: 1+2 +3 +14 213r2+4r3- 5x4 4x1+6r2 +8T3-...
Question 4. (20 pts.) a) In the following system of linear equations, find k such that the system Has unique solution Has infinitely many solutions Has no solution x+z=0 x + 2y + 2z = 3 (x + kk + 1)y + z = k Question 5. (20 pts.) a)Find Eigenvalues and Eigenvectors of the following matrix 13 2 6 1 -2 3 16 4 12 b) Find the Fourier series representation of the function with period 21 given by...
A third-order homogeneous linear equation and three linearly independent solutions are given below. Find a particular solution satisfying the given initial conditions. y (3) + 2y" - y' - 2y = 0; y(0) = 7, y' (0) = 16, y''O) = 0; e y2 = e-X, y3 = e - 2x Y The particular solution is y(x) = .
(1 point) Solving a system of linear ODEs with constant coefficients: Consider the system of equations x' = 3x – 2y y = 4x – 3y = -5x + 4y + 2z, with initial conditions x(0) = 1, y(0) = 2, 2(0) = 0. The matrix of the system is 13 -20 A= | 4 -3 0 1-5 4 2) and defining the column vector r(t) X(t) = y(t) z(t) we get that X' = AX, where X(0 = 2...
nsid r the following et ār vnctors. Let 1 v2 and V3 be column vectors in and let A be the 3 × 3 matrix v 1 v2 v③ with these vectors as its columns. The vi v2 and ] are linearly dependent if and nly the hom 9ene us linear system with augmented matrix 시 has a no tr ia solution Consider the following equation. 81-3-311 Solve for ci 2, andc3. If a nontrlvial solution exists, state it or...
Linear Algebra.
(1) Give three examples of a system of 3 equations with three variables, one with no solutions, one with a unique solutions and one with infinitely many solutions.
3. 30 pts For a specific reaction: AG = 10.0 kJ/mole at 27.0°C AG = 2.00 kJ/mole at 177°C Assuming that the enthalpies and entropies of formation are independent of temperature for this system, calculate AS (reaction) and AH (reaction). Is this reaction favorable at all temperatures? Favorable at some temperatures? Never favorable? Explain your answer including key temperatures, if appropriate, in <25 words.