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Are fi (x) = х, (x) = x2 , and f, (x) = 3x-8x2 linearly independent...
(16 points) Determine whether the given set of functions is linearly dependent or linearly independent on...
(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).
Are the functions fi (x) = ex+4 and fz(x-er-5 linearly dependent or independent? A. Linearty dependent...
Are the functions fi (x) = ex+4 and fz(x-er-5 linearly dependent or independent? A. Linearty dependent OB. Linearly independent Which of the following best describes the correct choice for part (a)? (Carefull) 0 A. Since the only solution to cfı + c/2 = 0 is ci = c2-0. B. Since the Wronskian equals zero for at least one x on (-o, o). C. Since the Wronskian never equals zero on (-oo, oo). D. Since the functions are scalar multiples of...
(Higher-order linear differential equations) (a) Show that yi (x)-z?, уг (z)-r3, and U3(z) = 1/x are linearly independe...
(Higher-order linear differential equations) (a) Show that yi (x)-z?, уг (z)-r3, and U3(z) = 1/x are linearly independent solutions of 3. хзу",-z?y"-2xy' + 6y-0 on (-oo, 0) and (0, +00). Write down the general solution to (4 (b) Find a fundamental set S of solutions of
(Higher-order linear differential equations) (a) Show that yi (x)-z?, уг (z)-r3, and U3(z) = 1/x are linearly independent solutions of 3. хзу",-z?y"-2xy' + 6y-0 on (-oo, 0) and (0, +00). Write down the general...
#1 part a and b please write solutions neatly 1. (16 points) Determine whether the given...
#1 part a and b please write solutions neatly
1. (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) f(x) = x + 2 cos?x, f?(x) = 3sin?x, f(x) = x+2 on (-0,0). (b) (8 points) f (x) = ed" and 12(x) = e 4s are solutions of the linear homogeneous differential equation y" + y' - 12y = 0 on (-0,0).
1. (16 points) Determine whether the given set of functions is linearly dependent or linearly independent...
1. (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) S(x) = x + 2cos?x, S2(x) = 3 sin’x, S(x) = x + 2 on (0,0). (b) (8 points) (x) = and f(x) = differential equation " + 1" 4x are solutions of the linear homogeneous O on () 12
Two linearly independent solutions of the differential equation y''+4y'+4y=0 are of Two linearly independent solutions the...
Two linearly independent solutions of the differential
equation y''+4y'+4y=0 are
of Two linearly independent solutions the differential equation are 2x y,=e Y2 = e 2x / - 2x 6 Y,=e 92= xe 2x @g, = e - 2x -2x , 92= xe 2x y = e 2x Y 2 = xe²x e 9,=02x 1 Y 2 = e- 2x
If the functions y = x and y = xe" are linearly independent solutions of the...
If the functions y = x and y = xe" are linearly independent solutions of the non-homogeneous second-order linear differential equation with variable coefficients z_ yll – x(x + 2)y + (x+2)y=r, its general solution is given by Oy=C1 + C2xe" + x2 O y=C1x + C2xe - 22 None of them O y=C12 + C2z²er - 23 Oy=C12? + Cymet – x3
The indicated functions are known linearly independent solutions of the associated homogeneous differential equation on (0,...
The indicated functions are known linearly independent solutions of the associated homogeneous differential equation on (0, 0). Find the general solution of the given nonhomogeneous equation. *?y" + xy' + (x2 - 1)y = x3/2; Y1 = x-1/2 cos(x), Y2 = x-1/2 sin(x) y(x) =
Question Find three linearly independent solutions of the given third-order differential equation and write a general...
Question Find three linearly independent solutions of the given third-order differential equation and write a general solution as an arbitrary linear combination of them. y-y"-21y' +5y 0 -0 A general solution is y(t)
Question 5 Is the set of functions linearly dependent or linearly independent? f(x) = 7, g(x)...
Question 5 Is the set of functions linearly dependent or linearly independent? f(x) = 7, g(x) = 5x +1, h(x) = 3x2 - 4x + 5 Linearly dependent Linearly independent Have no clue... Question 6 Given a solution to the DE below, find a second solution by using reduction of order. r’y' – 3xy + 5y = 0; y1 = r* cos(In x) y2 = xsin(In x) y2 = x2 sin Y2 = 2 * sin(In) . . y2 =...
(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).
Are the functions fi (x) = ex+4 and fz(x-er-5 linearly dependent or independent? A. Linearty dependent OB. Linearly independent Which of the following best describes the correct choice for part (a)? (Carefull) 0 A. Since the only solution to cfı + c/2 = 0 is ci = c2-0. B. Since the Wronskian equals zero for at least one x on (-o, o). C. Since the Wronskian never equals zero on (-oo, oo). D. Since the functions are scalar multiples of...
(Higher-order linear differential equations) (a) Show that yi (x)-z?, уг (z)-r3, and U3(z) = 1/x are linearly independent solutions of 3. хзу",-z?y"-2xy' + 6y-0 on (-oo, 0) and (0, +00). Write down the general solution to (4 (b) Find a fundamental set S of solutions of
(Higher-order linear differential equations) (a) Show that yi (x)-z?, уг (z)-r3, and U3(z) = 1/x are linearly independent solutions of 3. хзу",-z?y"-2xy' + 6y-0 on (-oo, 0) and (0, +00). Write down the general...
#1 part a and b please write solutions neatly
1. (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) f(x) = x + 2 cos?x, f?(x) = 3sin?x, f(x) = x+2 on (-0,0). (b) (8 points) f (x) = ed" and 12(x) = e 4s are solutions of the linear homogeneous differential equation y" + y' - 12y = 0 on (-0,0).
1. (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) S(x) = x + 2cos?x, S2(x) = 3 sin’x, S(x) = x + 2 on (0,0). (b) (8 points) (x) = and f(x) = differential equation " + 1" 4x are solutions of the linear homogeneous O on () 12
Two linearly independent solutions of the differential
equation y''+4y'+4y=0 are
of Two linearly independent solutions the differential equation are 2x y,=e Y2 = e 2x / - 2x 6 Y,=e 92= xe 2x @g, = e - 2x -2x , 92= xe 2x y = e 2x Y 2 = xe²x e 9,=02x 1 Y 2 = e- 2x
If the functions y = x and y = xe" are linearly independent solutions of the non-homogeneous second-order linear differential equation with variable coefficients z_ yll – x(x + 2)y + (x+2)y=r, its general solution is given by Oy=C1 + C2xe" + x2 O y=C1x + C2xe - 22 None of them O y=C12 + C2z²er - 23 Oy=C12? + Cymet – x3
The indicated functions are known linearly independent solutions of the associated homogeneous differential equation on (0, 0). Find the general solution of the given nonhomogeneous equation. *?y" + xy' + (x2 - 1)y = x3/2; Y1 = x-1/2 cos(x), Y2 = x-1/2 sin(x) y(x) =
Question Find three linearly independent solutions of the given third-order differential equation and write a general solution as an arbitrary linear combination of them. y-y"-21y' +5y 0 -0 A general solution is y(t)
Question 5 Is the set of functions linearly dependent or linearly independent? f(x) = 7, g(x) = 5x +1, h(x) = 3x2 - 4x + 5 Linearly dependent Linearly independent Have no clue... Question 6 Given a solution to the DE below, find a second solution by using reduction of order. r’y' – 3xy + 5y = 0; y1 = r* cos(In x) y2 = xsin(In x) y2 = x2 sin Y2 = 2 * sin(In) . . y2 =...
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