(1 point) Which of the following vectors forms a fundamental set of solutions to the system...
2. (5pts Determine whether the following set of vectors is a fundamental set of solutions of a system y' = Ay for some matrix A = A(t). / -et 0 y1 = -e- , y2 = -et, y3 = 0 I ett 2e-t 2e2
6. The vectors x-[)and X - [-] are solutions vectors corresponding to the system of differential equation X = AX (a) Use the Wronskian to show that X, and X, are linearly independent. (b) Write down a general solution to the system of equations. (e) Find the solution to the system subject to the initial condition X(0) -
Please solve using eigenvalues and vectors (Please do not use laplace transforms!) Please show all steps neatly and in detail, will rate quickly! 7. Find all the solutions to the following system of differential equations . ,-[1-21 7. Find all the solutions to the following system of differential equations . ,-[1-21
The vectors 3 X3 =|-6|+t|4 X2 х, =|-2|+ t 12 are solutions of a system X' = AX Determine whether the vectors form a fundamental set of solutions.
1. Write the forms of the series expansion about the regular singular point x=0 for two linearly independent solutions to the following differential equation (do not compute the coefficients in the expansions): zºy'(x) - xy'(x) + (1 - x)y(x) = 0. (1) 2. Does the following system of equations have an unique solution? Explain your reason for the answer (do not find the solution). 2x 1 + 4x2 + x3 = 8 2x + 4.62 = 6 -401 - 8x2...
Differential equations / which pair of functions below cannot be a fundrmental set of solutions? 6. Which pair of functions below cannot be a fundamental set of solutions? (8 Points) 1, x3, xinx 3 cost + 6 sint, 5 cost + 10 sint €2x cos 3x + sin 3x, 1 e-31 3 te-31 5et + 5, 2e + 1
6. Which pair of functions below cannot be a fundamental set of solutions? (8 Puan) 5e + 5, 2e + 2 e-21, te-21, 5 cost + 3 sint , 3 cost + sint e2%, cos 2x + sin 2x O1, x2, x2 In x
6. Which pair of functions below cannot be a fundamental set of solutions? * (8 Puan) O 1, x, x? Inx O 5e + 5, 2eX + 1 0 2x, cos 3x + sin 3x, 1 3 cost + 6 sint , 5 cost + 10 sint O e-31, te-31
Question 6 Express the solution of the following system of equations as a linear combination of complimentary and particular solutions. **( )x+(3) Question 7: Find the particular solution for the following system of differential equations. 6 6t X + on (2010) -10t+4 Question 8: Use Variation of Parameters method to find particular solution for the following system X': 1-3 X + 30 2 -4
(1 point) Find a set of vectors {u, v} in R4 that spans the solution set of the equations 0, I w - x - y + 4z | 4w + 2x – y – 2z = =