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a) they are linearly independent
b)they are linearly dependent
c)neither linearly dependent nor linearly independent
d)functions cannot be determined in real space x
e) none of them
Homework Answers
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a) they are linearly independent
b)they are linearly dependent
c)neither linearly dependent nor linearly independent
d)functions...
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 =...
Find linearly independent functions that are annihilated by the given differential operator. (Giv...
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)=____________
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...
(a) Are the functions h(a) 1,(z) cos (2z) and fs(z) sin(x) linearly independent? (b) How about...
(a) Are the functions h(a) 1,(z) cos (2z) and fs(z) sin(x) linearly independent? (b) How about the functions f(a)1, Ja(ar)sin (a) and fs(a)sin ()? Why or why Why or why not? not? (Hint: Plug in 3 different values of z to get a linear system for the coefficients in the definition of linear independence.)
17. Another way to check if y1, y2 are linearly INDEPENDENT in an interval I is:...
17. Another way to check if y1, y2 are linearly INDEPENDENT in
an interval I is:
for all I
for all I
does not exist for all I
d. none of the above
18. If y1 is a solution of the equation y "+ P (x) y '+ Q (x) y
= 0, a second solution would be y2 (x) = u (x) y1 (x) where u (x)
it is:
d. all of the above
19. The following set...
We already know the functions defined by y =C+a•f[b(x-d)] with the assumption that b>0. To see...
We already know the functions defined by y =C+a•f[b(x-d)] with the assumption that b>0. To see what happens when b<0, work parts (a)-(f) in order. (a) Use an even-odd identity to write y = sin(-2x) as a function of 2x. y= (b) How is your answer to part (a) related to y = sin(2x)? O It is the negative of y = sin (2x). olt equals y = sin (2x). (c) Use an even-odd identity to write y = cos(...
We already know the functions defined by y =c+a+f[b(x-d)] with the assumption that b>0. To see...
We already know the functions defined by y =c+a+f[b(x-d)] with the assumption that b>0. To see what happens when b<0, work parts (a)-(f) in order. (a) Use an even-odd identity to write y = sin (-2x) as a function of 2x. y = (b) How is your answer to part (a) related to y = sin (2x)? O It is the negative of y=sin (2x). It equals y=sin (2x). (c) Use an even-odd identity to write y = cos(-5x) as...
22.1 A,C depending on whether indefinite op de ol functions and an is never zero over...
22.1 A,C
depending on whether indefinite op de ol functions and an is never zero over this interval. Additional Exercises 22.1. Find the general solution to each of the following nonhomogeneous differential equations Use variation of parameters even if another method might seem easier. For your comve- nience, each equation is accompanied by a general solution to the corresponding homoge- neous equation a. ry" - 2xy' + 2y 3x, yn = cix + c2x2 b. y + y = cot(x)...
Let Coo denote the set of smooth functions, ie, functions f : R → R whose nth derivative exists, ...
Let Coo denote the set of smooth functions, ie, functions f : R → R whose nth derivative exists, for all n. Recall that this is a vector space, where "vectors" of Coo are function:s like f(t) = sin(t) or f(t) = te, or polynomials like f(t)-t2-2, or constant functions like f(t) = 5, and more The set of smooth functions f (t) which satisfy the differential equation f"(t) +2f (t) -0 for all t, is the same as the...
Problem 3. Let D be the vector space of all differentiable function R wth the usual pointwise add...
Problem 3. Let D be the vector space of all differentiable function R wth the usual pointwise addition and scalar multiplication of functions. In other words, for f, g E D and λ E R the function R defined by: (f +Ag) ()-f(r) +Ag(x) Let R be four functions defined by: s(x)-: sin 11 c(r) : cosz, co(z)--cos(z + θ), and so(r) sin(z + θ), and Wspanls, c Which of the following statements are true: (a) For each fixed θ...
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 =...
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...
(a) Are the functions h(a) 1,(z) cos (2z) and fs(z) sin(x) linearly independent? (b) How about the functions f(a)1, Ja(ar)sin (a) and fs(a)sin ()? Why or why Why or why not? not? (Hint: Plug in 3 different values of z to get a linear system for the coefficients in the definition of linear independence.)
17. Another way to check if y1, y2 are linearly INDEPENDENT in
an interval I is:
for all I
for all I
does not exist for all I
d. none of the above
18. If y1 is a solution of the equation y "+ P (x) y '+ Q (x) y
= 0, a second solution would be y2 (x) = u (x) y1 (x) where u (x)
it is:
d. all of the above
19. The following set...
We already know the functions defined by y =C+a•f[b(x-d)] with the assumption that b>0. To see what happens when b<0, work parts (a)-(f) in order. (a) Use an even-odd identity to write y = sin(-2x) as a function of 2x. y= (b) How is your answer to part (a) related to y = sin(2x)? O It is the negative of y = sin (2x). olt equals y = sin (2x). (c) Use an even-odd identity to write y = cos(...
We already know the functions defined by y =c+a+f[b(x-d)] with the assumption that b>0. To see what happens when b<0, work parts (a)-(f) in order. (a) Use an even-odd identity to write y = sin (-2x) as a function of 2x. y = (b) How is your answer to part (a) related to y = sin (2x)? O It is the negative of y=sin (2x). It equals y=sin (2x). (c) Use an even-odd identity to write y = cos(-5x) as...
22.1 A,C
depending on whether indefinite op de ol functions and an is never zero over this interval. Additional Exercises 22.1. Find the general solution to each of the following nonhomogeneous differential equations Use variation of parameters even if another method might seem easier. For your comve- nience, each equation is accompanied by a general solution to the corresponding homoge- neous equation a. ry" - 2xy' + 2y 3x, yn = cix + c2x2 b. y + y = cot(x)...
Let Coo denote the set of smooth functions, ie, functions f : R → R whose nth derivative exists, for all n. Recall that this is a vector space, where "vectors" of Coo are function:s like f(t) = sin(t) or f(t) = te, or polynomials like f(t)-t2-2, or constant functions like f(t) = 5, and more The set of smooth functions f (t) which satisfy the differential equation f"(t) +2f (t) -0 for all t, is the same as the...
Problem 3. Let D be the vector space of all differentiable function R wth the usual pointwise addition and scalar multiplication of functions. In other words, for f, g E D and λ E R the function R defined by: (f +Ag) ()-f(r) +Ag(x) Let R be four functions defined by: s(x)-: sin 11 c(r) : cosz, co(z)--cos(z + θ), and so(r) sin(z + θ), and Wspanls, c Which of the following statements are true: (a) For each fixed θ...
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