Find the Wronskian of the given functions and determine if the functions are independent or linearly...
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...
(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
Find linearly independent functions that are annihilated by the given differential operator. (Give as many functions as possible. Use x as the independent variable. Enter your answers as a comma-separated list.) 1. D4 2. D2 − 7D − 44 Solve the given initial-value problem: 2. y'' + y = 10 cos 2x − 4 sin x, y(π/2) = −1, y'(π/2) = 0 : y(x)=____________
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...
Determine whether the given set of functions is linearly independent on the interval (-00,00) fı(x) = xf2(x) = sin(x) $3(x) = sin(2x)
Determine whether the given set of functions is linearly independent on the interval (−∞, ∞) f1(x) = x f2(x) = sin(x) f3(x) = sin(2x)
(3) Determine whether the given set of functions is linearly independent on the interval (-00,00) f1(x) = x f2(x) = sin(x) $3(x) = sin(2x)
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. Compute the Wronskian of the functions 3e3t and -2e2t and use it to determine whether or not they are linearly independent. Explain how you use the Wronksian to determine this.
(16 points) Determine whether the given set of functions is linearly dependent or linearly independent on the indicated interval. Justify your answers. (a) (8 points) fi(x) = x + 2cos²x, f(x) = 3sin’x, f(x) = x + 2 on (-0,co). (b) (8 points) fi(x) = e34 and 12(x) = e 4x are solutions of the linear homogeneous differential equation y" + y' - 12y = 0 on (-0,co).