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a. 1. Answer each of the following: Compute the Wrornskian of the set {ex cos 3x,...
1. Answer each of the following: a. Compute the Wrornskian of the set {e* cos 3x,...
1. Answer each of the following: a. Compute the Wrornskian of the set {e* cos 3x, e* sin 3x} b. Show that {e* cos 3x, e* sin 3x} form a fundamental solution set for y" - 2y' +10y = 0 on the interval (-00,-) and write the general solution
Please show all work with clear handwriting a) Compute the Wrornskian of the set {e* cos...
Please show all work with clear handwriting
a)
Compute the Wrornskian of the set {e* cos 3x, ex sin 3x} b. Show that {ex cos 3x, ex sin 3x} form a fundamental solution set for y" – 2y' +10y = 0 on the interval (-00,00) and write the general solution
You are given that yh = c1 cos(3x) +c2 sin(3x) is the general solution to the...
You are given that yh = c1 cos(3x) +c2 sin(3x) is the general
solution to the homogeneous differential equation y 00 + 9y = 0 (a)
In each case below, write down your “guess” for the form of the
particular solution to the differential equation. y 00 + 9y =
f(x)
Question 6. (Total marks: 14) You are given that y = cos(3x) + sin(3.c) is the general solution to the homogeneous differential equation y" +9y = 0 (a) In...
Please show solutions. Answer: 1. Find a general solution to the following differential equations: (a) y"...
Please show solutions.
Answer:
1. Find a general solution to the following differential equations: (a) y" + y = 0 (b) y" – 2y' + 264 = 0 (c) 4x²y" – 3y = 0 (d) y" + 4y = 9 sin(t). (e) y" – 6y' + 9y = 6e3x 1. (a) y = ci + c2e- (b) y = cle' cos(5t) + czet sin(5t) (c) y = cit-1/2 + c2t3/2 (d) y = ci cos(2t) + c2 sin(2t) + 3...
Solve the following questions and Choose the correct answer. 1) The General solution to y" +...
Solve the following questions and Choose the correct answer. 1) The General solution to y" + y = 0 sty -3&y(x) = -3 y = cos(3x) + sin(-31) , 3cos(x) – 3 sin(x) 3 ) 3 Answer 2) Suppose that y(t) and y(t) are two solutions of a certain second order linear differential equation, sin(t)y" + cos(t) y' - y = 0. 0<<< What is the general form of the Wronskian Wy ) (6) ? Without solving the equation. b)...
1. For each question: i) verify that yı(2) is a solution. ii) Use reduction of order...
1. For each question: i) verify that yı(2) is a solution. ii) Use reduction of order to find the general solution. iii) Find a fundamental solution set. iv) Find the Wronkskian, and list it's zeroes and discontinuities. Verify that the Wronskian is nonzero and continuous on the given interval. (e) y" + 4y + 4y = 0, yı = -2% (-00,00). () r’y" – 2xy' + 2y = 0, yı = x. (0,00). -
please answer alll! its greatly appreicated Find a general solution. u" + 33u = 0 u(t)...
please answer alll! its greatly appreicated
Find a general solution. u" + 33u = 0 u(t) = [. Solve the given initial value problem. y"' + 2y' +10y = 0; y(0) = 4, y'(0) = - 3 y(t) = Use the annihilator method to determine the form of a particular solution for the given equation V'+w-20 = cos(-3x) + 11 Find a differential operator that will annihilate the nonhomogeneity cos ( - 3x) + 11. (Type the lowest-order annihilator that...
II. Determine the general solution of the given 2nd order linear homogeneous equation. 1. y" -...
II. Determine the general solution of the given 2nd order linear homogeneous equation. 1. y" - 2y' + 3y = 0 (ans. y = ci e' cos V2 x + C2 e* sin V2 x) 2. y" + y' - 2y = 0 (ans. y = C1 ex + C2 e -2x) 3. y" + 6y' + 9y = 0 (ans. y = C1 e 3x + c2x e-3x) 4. Y" + 4y = 0, y(t) = 0, y'(T) =...
1. Find the solution set for each of the following on the interval - 27 x...
1. Find the solution set for each of the following on the interval - 27 x < 2 A. secx = 2 B. 5 sino - 3 = sin - 5 C. 3tan? = 1 D. sinr = cos E sin cos 7 = r = - sin 2. Find the solution set for each of the following on the interval 0 <r <2 A. COSI = cos x B. 2 sinr = sin C. 2 sinx: - sin x...
(1 point) Given the fourth order homogeneous constant coefficient equation y' + 10y" + 9y =...
(1 point) Given the fourth order homogeneous constant coefficient equation y' + 10y" + 9y = 0 1) the auxiliary equation is ar4 + bp3 + cp2 + dr te= r^(4)+10r^2+9 0. 2) The roots of the auxiliary equation are 1,-1,31,-3i (enter answers as a comma separated list). 3) A fundamental set of solutions is cosx,sinx,cos(3x), sin(3x) (Enter the fundamental set as a commas separated list 41, 42, 43, 44). Therefore the general solution can be written as y =...
1. Answer each of the following: a. Compute the Wrornskian of the set {e* cos 3x, e* sin 3x} b. Show that {e* cos 3x, e* sin 3x} form a fundamental solution set for y" - 2y' +10y = 0 on the interval (-00,-) and write the general solution
Please show all work with clear handwriting
a)
Compute the Wrornskian of the set {e* cos 3x, ex sin 3x} b. Show that {ex cos 3x, ex sin 3x} form a fundamental solution set for y" – 2y' +10y = 0 on the interval (-00,00) and write the general solution
You are given that yh = c1 cos(3x) +c2 sin(3x) is the general
solution to the homogeneous differential equation y 00 + 9y = 0 (a)
In each case below, write down your “guess” for the form of the
particular solution to the differential equation. y 00 + 9y =
f(x)
Question 6. (Total marks: 14) You are given that y = cos(3x) + sin(3.c) is the general solution to the homogeneous differential equation y" +9y = 0 (a) In...
Please show solutions.
Answer:
1. Find a general solution to the following differential equations: (a) y" + y = 0 (b) y" – 2y' + 264 = 0 (c) 4x²y" – 3y = 0 (d) y" + 4y = 9 sin(t). (e) y" – 6y' + 9y = 6e3x 1. (a) y = ci + c2e- (b) y = cle' cos(5t) + czet sin(5t) (c) y = cit-1/2 + c2t3/2 (d) y = ci cos(2t) + c2 sin(2t) + 3...
Solve the following questions and Choose the correct answer. 1) The General solution to y" + y = 0 sty -3&y(x) = -3 y = cos(3x) + sin(-31) , 3cos(x) – 3 sin(x) 3 ) 3 Answer 2) Suppose that y(t) and y(t) are two solutions of a certain second order linear differential equation, sin(t)y" + cos(t) y' - y = 0. 0<<< What is the general form of the Wronskian Wy ) (6) ? Without solving the equation. b)...
1. For each question: i) verify that yı(2) is a solution. ii) Use reduction of order to find the general solution. iii) Find a fundamental solution set. iv) Find the Wronkskian, and list it's zeroes and discontinuities. Verify that the Wronskian is nonzero and continuous on the given interval. (e) y" + 4y + 4y = 0, yı = -2% (-00,00). () r’y" – 2xy' + 2y = 0, yı = x. (0,00). -
please answer alll! its greatly appreicated
Find a general solution. u" + 33u = 0 u(t) = [. Solve the given initial value problem. y"' + 2y' +10y = 0; y(0) = 4, y'(0) = - 3 y(t) = Use the annihilator method to determine the form of a particular solution for the given equation V'+w-20 = cos(-3x) + 11 Find a differential operator that will annihilate the nonhomogeneity cos ( - 3x) + 11. (Type the lowest-order annihilator that...
II. Determine the general solution of the given 2nd order linear homogeneous equation. 1. y" - 2y' + 3y = 0 (ans. y = ci e' cos V2 x + C2 e* sin V2 x) 2. y" + y' - 2y = 0 (ans. y = C1 ex + C2 e -2x) 3. y" + 6y' + 9y = 0 (ans. y = C1 e 3x + c2x e-3x) 4. Y" + 4y = 0, y(t) = 0, y'(T) =...
1. Find the solution set for each of the following on the interval - 27 x < 2 A. secx = 2 B. 5 sino - 3 = sin - 5 C. 3tan? = 1 D. sinr = cos E sin cos 7 = r = - sin 2. Find the solution set for each of the following on the interval 0 <r <2 A. COSI = cos x B. 2 sinr = sin C. 2 sinx: - sin x...
(1 point) Given the fourth order homogeneous constant coefficient equation y' + 10y" + 9y = 0 1) the auxiliary equation is ar4 + bp3 + cp2 + dr te= r^(4)+10r^2+9 0. 2) The roots of the auxiliary equation are 1,-1,31,-3i (enter answers as a comma separated list). 3) A fundamental set of solutions is cosx,sinx,cos(3x), sin(3x) (Enter the fundamental set as a commas separated list 41, 42, 43, 44). Therefore the general solution can be written as y =...
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