Homework Answers
3t Two solutions to y'' – y' - 12y = 0 are yı = e 12...
3t Two solutions to y'' – y' - 12y = 0 are yı = e 12 = en a) Find the Wronskian. W = Preview b) Find the solution satisfying the initial conditions y(0) = 0, y'(0) = 42 y = Preview
3 Question 25 Given a set of DE solutions: y1(x) = e* cos x and y2(x)...
3 Question 25 Given a set of DE solutions: y1(x) = e* cos x and y2(x) = e sinx, a) Find the value of the Wronskian W[ v1.y2). b) Determine if the solutions Y1, Y2 are linearly independent. a)W=e b) Linearly Independent a) W=-ex b) Linearly Independent O a) W = 1 b) Linearly Independent a) W=eX b) Linearly Dependent O a) W=0 b) Linearly Dependent None of them
Two linearly independent solutions of the differential equation y" - 5y' + 6y = 0 are...
Two linearly independent solutions of the differential equation y" - 5y' + 6y = 0 are Select the correct answer. a. Y1 = 62, y2 = 232 b. Y1 = 0 -6x, y2 = e** c. Y1 = e-Gx, y2 = et d. Y1 = 0-2, y2 = 2-3x e. Yi = e6x, y2 = e-*
Bonus (Abel's formula) a) Show that if y1 and y2 are solutions to the differential equation...
Bonus (Abel's formula) a) Show that if y1 and y2 are solutions to the differential equation y"p(t)y(t)y 0 where p and q are continuous on an interval I, then the Wronskian of y and y2, W(y1,y2) (t) is given by - Sp(t)dt ce W(y1, y2)(t) where c depends on y and y2 (b) Use Abel's formula to find the Wronskian of two solutions to the differential equation ty"(t 1)y 3y 0 Do not solve the differential equation
find Y1=, Y2=, and W(t)= (1 point) Find the function yi of t which is the...
find Y1=, Y2=, and W(t)=
(1 point) Find the function yi of t which is the solution of 25y" – 40y' + 12y = 0 y(0) = 1, yf(0) = 0. with initial conditions Yi = Find the function y2 of t which is the solution of 25y" – 40y' + 12y = 0 with initial conditions Y2 = Find the Wronskian W(t) = W(y1, y2). W(t) = Remark: You can find W by direct computation and use Abel's theorem...
Three linearly independent solutions of the differential equation y'"' - y" - 6y' = 0 are...
Three linearly independent solutions of the differential equation y'"' - y" - 6y' = 0 are Select the correct answer. a. V1 =e-6s, y2 =xe-1, V3 =1 b. Y1 = 224, y2 = 2-3x, y3 = 1 c. Y1 = 2-6x, y2 = e", y3 = 1 d. Y1 = e3x, y2 = 2-2*, y3 = 1 e. Vi=e , y2=xe-1, V3=1
Two linearly independent solutions of the differential equation y" + 4y' + 5y = 0 are...
Two linearly independent solutions of the differential equation y" + 4y' + 5y = 0 are Select the correct answer. a. Y1 = e-cos(2x), y2 = eʼsin (2x) b. Y1 = e-*, y2 = e-S* c. Yi= e-*cos(2x), y1=e-* sin(2x) d. Y1 = e-2xcosx, x, y2 = e–2*sinx e. Y1 = e', y2 = 5x
Two linearly independent solutions of the differential y" - 4y' + 5y = 0 equation are...
Two linearly independent solutions of the differential y" - 4y' + 5y = 0 equation are Select the correct answer. 7 Oa yı = e-*cos(2x), Y1 = e-*sin(2x) Ob. Y1 = et, y2 = ex Oc. yı = e cos(2x), y2 = e* sin(2x) Od. yı=e2*cosx, y2 = e2*sinx Oe. y = e-*, y2 = e-S*
Consider the ordinary differential equation: t2y" + 3ty' +y = 0. 1 (3 points) e) Use...
Consider the ordinary differential equation: t2y" + 3ty' +y = 0. 1 (3 points) e) Use Abel's formula to find the Wronskian of any two solutions of this equation and W[y1,y2](t). What do you observe? compare it to = t1 and y2(t) = t-1 nt represent a fundamental set of solu f) (2 points) Determine if y1 (t) tions (2 points) Find the general solution of t2y" +3ty' +y = 0. g) Solve the initial value problem t2y" + 3ty/...
Consider the differential equation, L[y] = y'' + p(t)y' + q(t)y = 0, (1) whose coefficients...
Consider the differential
equation, L[y] = y'' + p(t)y' + q(t)y = 0, (1) whose coefficients p
and q are continuous on some open interval I. Choose some point t0
in I. Let y1 be the solution of equation (1) that also satisfies
the initial conditions y(t0) = 1, y'(t0) = 0, and let y2 be the
solution of equation (1) that satisfies the initial conditions
y(t0) = 0, y'(t0) = 1. Then y1 and y2 form a fundamental set...
3t Two solutions to y'' – y' - 12y = 0 are yı = e 12 = en a) Find the Wronskian. W = Preview b) Find the solution satisfying the initial conditions y(0) = 0, y'(0) = 42 y = Preview
3 Question 25 Given a set of DE solutions: y1(x) = e* cos x and y2(x) = e sinx, a) Find the value of the Wronskian W[ v1.y2). b) Determine if the solutions Y1, Y2 are linearly independent. a)W=e b) Linearly Independent a) W=-ex b) Linearly Independent O a) W = 1 b) Linearly Independent a) W=eX b) Linearly Dependent O a) W=0 b) Linearly Dependent None of them
Two linearly independent solutions of the differential equation y" - 5y' + 6y = 0 are Select the correct answer. a. Y1 = 62, y2 = 232 b. Y1 = 0 -6x, y2 = e** c. Y1 = e-Gx, y2 = et d. Y1 = 0-2, y2 = 2-3x e. Yi = e6x, y2 = e-*
Bonus (Abel's formula) a) Show that if y1 and y2 are solutions to the differential equation y"p(t)y(t)y 0 where p and q are continuous on an interval I, then the Wronskian of y and y2, W(y1,y2) (t) is given by - Sp(t)dt ce W(y1, y2)(t) where c depends on y and y2 (b) Use Abel's formula to find the Wronskian of two solutions to the differential equation ty"(t 1)y 3y 0 Do not solve the differential equation
find Y1=, Y2=, and W(t)=
(1 point) Find the function yi of t which is the solution of 25y" – 40y' + 12y = 0 y(0) = 1, yf(0) = 0. with initial conditions Yi = Find the function y2 of t which is the solution of 25y" – 40y' + 12y = 0 with initial conditions Y2 = Find the Wronskian W(t) = W(y1, y2). W(t) = Remark: You can find W by direct computation and use Abel's theorem...
Three linearly independent solutions of the differential equation y'"' - y" - 6y' = 0 are Select the correct answer. a. V1 =e-6s, y2 =xe-1, V3 =1 b. Y1 = 224, y2 = 2-3x, y3 = 1 c. Y1 = 2-6x, y2 = e", y3 = 1 d. Y1 = e3x, y2 = 2-2*, y3 = 1 e. Vi=e , y2=xe-1, V3=1
Two linearly independent solutions of the differential equation y" + 4y' + 5y = 0 are Select the correct answer. a. Y1 = e-cos(2x), y2 = eʼsin (2x) b. Y1 = e-*, y2 = e-S* c. Yi= e-*cos(2x), y1=e-* sin(2x) d. Y1 = e-2xcosx, x, y2 = e–2*sinx e. Y1 = e', y2 = 5x
Two linearly independent solutions of the differential y" - 4y' + 5y = 0 equation are Select the correct answer. 7 Oa yı = e-*cos(2x), Y1 = e-*sin(2x) Ob. Y1 = et, y2 = ex Oc. yı = e cos(2x), y2 = e* sin(2x) Od. yı=e2*cosx, y2 = e2*sinx Oe. y = e-*, y2 = e-S*
Consider the ordinary differential equation: t2y" + 3ty' +y = 0. 1 (3 points) e) Use Abel's formula to find the Wronskian of any two solutions of this equation and W[y1,y2](t). What do you observe? compare it to = t1 and y2(t) = t-1 nt represent a fundamental set of solu f) (2 points) Determine if y1 (t) tions (2 points) Find the general solution of t2y" +3ty' +y = 0. g) Solve the initial value problem t2y" + 3ty/...
Consider the differential
equation, L[y] = y'' + p(t)y' + q(t)y = 0, (1) whose coefficients p
and q are continuous on some open interval I. Choose some point t0
in I. Let y1 be the solution of equation (1) that also satisfies
the initial conditions y(t0) = 1, y'(t0) = 0, and let y2 be the
solution of equation (1) that satisfies the initial conditions
y(t0) = 0, y'(t0) = 1. Then y1 and y2 form a fundamental set...
Most questions answered within 3 hours.
-
Where is the error in this code sequence?
String s1 = "Hello";
String s2 = "ello";...
asked 10 months ago -
Financial data for Joel de Paris, Inc., for last year
follow:
Joel de Paris, Inc.
Balance...
asked 10 months ago -
Consider this reaction:
Al2(SO4)3 (aq)+ BaCl3
(aq) Al2Cl6 (aq)- +
3BaSO4(s) . What is the...
asked 10 months ago -
Suppose that Savneet is considering increasing her
recent random sample from 20 car rentals to 40...
asked 10 months ago -
Trucks arrive at an unloading terminal at an average rate of 120
per hour.
Trucks arrive...
asked 10 months ago -
Why are methanol and ethanol completely soluble in water while
octanol is not very little soluble....
asked 10 months ago -
A facilities manager at a university reads in a research report
that the mean amount of...
asked 10 months ago -
When the CuSO4 is rehydrated by adding water to the anhydrous
compound, is this an endothermic...
asked 10 months ago -
A ray of sunlight is passing from diamond into crown glass; the
angle of incidence is...
asked 10 months ago -
A block of mass 0.249 kg is placed on top of a light, vertical
spring of...
asked 10 months ago -
how do the kidneys compensate in the presences of acidosis
a) trigger hyperventilate
b) reserve acid...
asked 10 months ago -
Question 501 pts
The rental rate of capital to the firm increases. Which of the
following...
asked 10 months ago