1. Compute the Wronskian of the functions 3e3t and -2e2t and use it to determine whether...
1. Compute the Wronskian for the following functions. Then use the Wronskian to determine whether the functions are linearly independant or linearly dependant. a) {(tan2x - sec2 x),3 (b) le,e,e) 2. Use variation of parameters to find a general solution to 2y" -4ry 6y3 1 given that y 2 and y2- 3 are linearly independant solutions of the associated homogeneous equation. (Hint: be careful the equations are in the right form.) Find a particular solution for each of the following...
Find the Wronskian of the given functions and determine if the functions are independent or linearly dependant linearly y1yx+3 y =2x-5
Ch3.2- Existence Uniqueness Wronskian: Problem 3 Previous Problem Problem List Next Problem (1 point) Use the Wronskian to determine whether the functions yı = sin(62) and y2 = cos(4.c) are linearly independent. Wronskian = det These functions are linearly independent because the Wronskian is nonzero for Choose value(s) of 2.
step by step please Without the aid of the Wronskian, determine whether the given set of functions is linearly independent or linearly dependent on the indicated interval. (a) (%) = In x, f(x) = Inx",(0, ) linearly dependent linearly independent (b) (x) = 2x",,(*) - +, n = 1, 2, Vdots, (-,) linearly dependent linearly independent (c) (X) = x, f(x) - X+4.(-.,-) linearly dependent linearly independent ,) (d) {(x) = cos(x + 2), f(x) - sinx, ( linearly dependent...
(1 point) Calculate the Wronskian for the following set of functions: f1(x) = 0, f2(2) = 2.c +5, f3(2) = 1e" + b W(fi(2), f2(2), f3()) NO_ANSWER 1. Is the above set of functions linearly independent or dependent?
Consider the vectors х() 3 (, 1)T х°() — (?, 26)Т. and i) Compute the Wronskian of X1 and X2 at t ii) In what intervals are X1 and X2 linearly independent? iii What conclusion can be drawn about the coefficients in the systems of homogeneous differential equation satisfied by X1 and X2? v) Find this system of equations and verify the conclusions of part iii Consider the vectors х() 3 (, 1)T х°() — (?, 26)Т. and i) Compute...
Determine whether the given functions are linearly dependent or linearly independent on the specified interval. Justify your decision. Thank you! Determine whether the given functions are linearly dependent or linearly independent on the specified interval. Justify your decision. {e 3*, e5x, 27x} on (-00,00) e Select the correct choice below and, if necessary, fill in the answer box to complete your choice. 3x 5x + =e and C2 A. The functions are linearly dependent because for constant values, C1 and...
(1) Calculate the Wronskian of the following vectors and determine if they are pointwise linearly independent or dependent. e 0 0 y(1) ). y (2) y (3) 3e- 3e24 6e2.c 2e34 0 W(y(1), y(2), y(3) Circle One: Independent Dependent
12. -/1 POINTS ZILLDIFFEQ8 4.1.017. Determine whether the given set of functions is linearly independent on the interval (-00,00). f(x) = 5, f(x) = cos2x, 13(x) = sinºx O linearly dependent O linearly independent Need Help? Read It Talk to a Tutor)
Determine whether the following set of functions on R is linearly independent: {1 + x, x + x 2 , x2 + x 3 , x3 + 1} .