. What do you obs](http://img.homeworklib.com/questions/7d8b8ef0-3c1c-11eb-a420-df8547bd60b6.png?x-oss-process=image/resize,w_560)
Homework Answers
Add Answer to:
Consider the ordinary differential equation: t2y" + 3ty' +y = 0. 1 (3 points) e) Use...
3 Consider the ordinary differential equation: ty +3tyy 0. e) (2 points) Find the Wronskian Wly,...
3 Consider the ordinary differential equation: ty +3tyy 0. e) (2 points) Find the Wronskian Wly, yal(t). f) (2 points) Calculate e I podt and compare it to Wl vlt). What do you observe? Does y1(t) = t-1 and y2(t) = t-11nt represent a fundamental set of solutions? g) (2 points) Why? h) (2 points) Find the general solution of ty" +3ty'y 0 İ) (4 points) Solve the initial value problem t2y't3ty'+y = 0, t > 0 with y(1) =...
(3) Consider the differential equation ty' + 3ty + y = 0, 1 > 0. (a)...
(3) Consider the differential equation ty' + 3ty + y = 0, 1 > 0. (a) Check that y(t) = 1-1 is a solution to this equation. (b) Find another solution (t) such that yı(t) and (t) are linearly independent (that is, wit) and y(t) form a fundamental set of solutions for the differential equation).
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
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...
Consider the differential equation e24 y" – 4y +4y= t> 0. t2 (a) Find T1, T2,...
Consider the differential equation e24 y" – 4y +4y= t> 0. t2 (a) Find T1, T2, roots of the characteristic polynomial of the equation above. 11,12 M (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. yı(t) M y2(t) = M (C) Find the Wronskian of the fundamental solutions you found in part (b). W(t) M (d) Use the fundamental solutions you found in (b) to find functions ui and Usuch...
b) (2 points) Determine the largest interval in which the solution of t2y"+3ty +y 0, with...
b) (2 points) Determine the largest interval in which the solution of t2y"+3ty +y 0, with y(1) = 0 and y'(1)-1 is certain to exist, without solving this initial value problem
If y is a known nonvanishing solution of y" p(t)y + q(t)y 0, then a second...
If y is a known nonvanishing solution of y" p(t)y + q(t)y 0, then a second solution y2 satisfies 2 У1? where W(y1, y2) is the Wronskian of y1 and y2. To determine y2, use Abel's formula, W(y1, Y2)(t) =C.eJP(t) dt, where C is certain constant that depends on y1 and y2, but not on t. Use the method above o find a second independent solution of the given equation. (х — 1)у" - ху" + у %3D 0, x>...
(1 point) It can be shown that h-e® and y2-e 9z are solutions to the differential...
(1 point) It can be shown that h-e® and y2-e 9z are solutions to the differential equation on the interval (-oo, oo) Find the Wronskian of y1,3/2 (Note the order matters) Do the functions y1, 32 form a fundamental set on -oo, 0o)? Answer should be yes or no
For the differential equation in) pin -1) + ... + Polly with solutions ....Yo Abel's formula...
For the differential equation in) pin -1) + ... + Polly with solutions ....Yo Abel's formula for the Wronskian is Wy ... (t) = cel ot Consider the equation (4) - y 0 . (a) Use Abel's formula from above to find the Wronskian of a fundamental set of solutions of the given equation. (Use as the constant mentioned in Abel's formula.) w(t) ce el cost, and sint. (b) Determine the Wronskian of the solutions d Wel, e, cost, sin...
Consider the differential equation y" – 7y + 12 y = 0. (a) Find r1, 72,...
Consider the differential equation y" – 7y + 12 y = 0. (a) Find r1, 72, roots of the characteristic polynomial of the equation above. 11,2 M (b) Find a set of real-valued fundamental solutions to the differential equation above. yı(t) M y2(t) M (C) Find the solution y of the the differential equation above that satisfies the initial conditions y(0) = -4, y'(0) = 1. g(t) = M Consider the differential equation y" – 64 +9y=0. (a) Find r1...
3 Consider the ordinary differential equation: ty +3tyy 0. e) (2 points) Find the Wronskian Wly, yal(t). f) (2 points) Calculate e I podt and compare it to Wl vlt). What do you observe? Does y1(t) = t-1 and y2(t) = t-11nt represent a fundamental set of solutions? g) (2 points) Why? h) (2 points) Find the general solution of ty" +3ty'y 0 İ) (4 points) Solve the initial value problem t2y't3ty'+y = 0, t > 0 with y(1) =...
(3) Consider the differential equation ty' + 3ty + y = 0, 1 > 0. (a) Check that y(t) = 1-1 is a solution to this equation. (b) Find another solution (t) such that yı(t) and (t) are linearly independent (that is, wit) and y(t) form a fundamental set of solutions for 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
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...
Consider the differential equation e24 y" – 4y +4y= t> 0. t2 (a) Find T1, T2, roots of the characteristic polynomial of the equation above. 11,12 M (b) Find a set of real-valued fundamental solutions to the homogeneous differential equation corresponding to the one above. yı(t) M y2(t) = M (C) Find the Wronskian of the fundamental solutions you found in part (b). W(t) M (d) Use the fundamental solutions you found in (b) to find functions ui and Usuch...
b) (2 points) Determine the largest interval in which the solution of t2y"+3ty +y 0, with y(1) = 0 and y'(1)-1 is certain to exist, without solving this initial value problem
If y is a known nonvanishing solution of y" p(t)y + q(t)y 0, then a second solution y2 satisfies 2 У1? where W(y1, y2) is the Wronskian of y1 and y2. To determine y2, use Abel's formula, W(y1, Y2)(t) =C.eJP(t) dt, where C is certain constant that depends on y1 and y2, but not on t. Use the method above o find a second independent solution of the given equation. (х — 1)у" - ху" + у %3D 0, x>...
(1 point) It can be shown that h-e® and y2-e 9z are solutions to the differential equation on the interval (-oo, oo) Find the Wronskian of y1,3/2 (Note the order matters) Do the functions y1, 32 form a fundamental set on -oo, 0o)? Answer should be yes or no
For the differential equation in) pin -1) + ... + Polly with solutions ....Yo Abel's formula for the Wronskian is Wy ... (t) = cel ot Consider the equation (4) - y 0 . (a) Use Abel's formula from above to find the Wronskian of a fundamental set of solutions of the given equation. (Use as the constant mentioned in Abel's formula.) w(t) ce el cost, and sint. (b) Determine the Wronskian of the solutions d Wel, e, cost, sin...
Consider the differential equation y" – 7y + 12 y = 0. (a) Find r1, 72, roots of the characteristic polynomial of the equation above. 11,2 M (b) Find a set of real-valued fundamental solutions to the differential equation above. yı(t) M y2(t) M (C) Find the solution y of the the differential equation above that satisfies the initial conditions y(0) = -4, y'(0) = 1. g(t) = M Consider the differential equation y" – 64 +9y=0. (a) Find r1...
Most questions answered within 3 hours.
-
Suppose, for any future year, the probability its October rain
is more than 3 inches is...
asked 53 seconds ago -
Solve the following systems of linear equations using
substitution 12p + 3q = 15 6q +...
asked 8 minutes ago -
Prof. D went grocery shopping and purchased one dozen eggs and
one pound of flour (all...
asked 15 minutes ago -
If
somehow loop of Henle were removed - that is if the proximal tubule
was connected...
asked 15 minutes ago -
Add 1ml of 0.18M of HCl (aq) to 1ml of 0.2M of [Ag(NH3)2]Br
(aq).
Write the...
asked 22 minutes ago -
1. Smoke detectors use Am-241, an alpha emitter, to detect smoke
particles. A parent is concerned...
asked 27 minutes ago -
Scenario: Web application developed to capture customers
demographic and financial information for filling their taxes. This...
asked 30 minutes ago -
Which of the following statements are true?
1. Glass is mostly silicon dioxide and so when...
asked 52 minutes ago -
Korman Company has the following securities in its portfolio of
equity securities on December 31, 2018:...
asked 53 minutes ago -
Using the 12th edition of Language Awareness,
complete the following assignment:
After reading Akiba Solomon's "Thugs....
asked 1 hour ago -
For all problems assume an effective monthly interest rate of 1%
unless otherwise indicated in the...
asked 1 hour ago -
Fix all syntax and logical errors for the following program.
Please generate the correct output. //...
asked 1 hour ago