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find Y1=, Y2=, and W(t)=
(1 point) Find the function yi of t which is the...
(1 point) Find the function yn oft which is the solution of 494" – 9y =...
(1 point) Find the function yn oft which is the solution of 494" – 9y = 0 y(0) = 1, 41(0) = 0. with initial conditions Yi = Find the function y of t which is the solution of 49y" – 9y = 0 with initial conditions Y2 = y2(0) = 0, $(0) = 1. Find the Wronskian W(t) = W(41, 42). (Hint: write y, and y2 in terms of hyperbolic sine and cosine and use properties of the hyperbolic...
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
Please prove this solution and explain why y2 can be taken as (x^2)(y1) Problem 2. Find the general solution of the equation Note that one of two linearly independent solutions is yi(r) -e. Solution....
Please prove this solution and explain why y2 can be taken as
(x^2)(y1)
Problem 2. Find the general solution of the equation Note that one of two linearly independent solutions is yi(r) -e. Solution. Using Abel's formula, we get the following relations for the Wronskian dW pi dW 2r1 On the other hand, Comparing these two expression for W(x), we can take y2 :- r2yı. Correspondingly, the general solution is
Problem 2. Find the general solution of the equation Note...
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 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/...
A) Assume that y1(c) t and y2)te are solutions of the differential equation t2y_ t(t + 2))" + t(t...
a) Assume that y1(c) t and y2)te are solutions of the differential equation t2y_ t(t + 2))" + t(t + 2)y-0, t > 0 Do y1(t) and y2() form a fundamental set of solutions of the O.D.E.? C) State the general solution for this O.D.E.
a) Assume that y1(c) t and y2)te are solutions of the differential equation t2y_ t(t + 2))" + t(t + 2)y-0, t > 0 Do y1(t) and y2() form a fundamental set of solutions of...
Two solutions to y' + 6y + 25 = 0 are y1 = = e 3t...
Two solutions to y' + 6y + 25 = 0 are y1 = = e 3t sin(4t), y2 = e cos( 4t). a) Find the Wronskian. W b) Find the solution satisfying the initial conditions y(0) = - 4, y'(0) = 0 y =
yi 24 The joint probability function of Y1 and Y2 is given. 0 1/8 3/8 Y2...
yi 24 The joint probability function of Y1 and Y2 is given. 0 1/8 3/8 Y2 1 2/8 1/8 3 0 1/8 Find (a) Cov(Y1, Y2) and (b) the correlation coefficient p of Y, and Y2.
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-find the recurrence relation using power series solutions. 2-find the first four terms in each of...
1-find the recurrence relation using power series
solutions.
2-find the first four terms in each of two solutions y1 and
y2
3-by evaluating wronskian w(y1,y2) show that they from a
fundamental solution set.
Iy yry 0, zo = 1
(1 point) Find the function yn oft which is the solution of 494" – 9y = 0 y(0) = 1, 41(0) = 0. with initial conditions Yi = Find the function y of t which is the solution of 49y" – 9y = 0 with initial conditions Y2 = y2(0) = 0, $(0) = 1. Find the Wronskian W(t) = W(41, 42). (Hint: write y, and y2 in terms of hyperbolic sine and cosine and use properties of the hyperbolic...
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
Please prove this solution and explain why y2 can be taken as
(x^2)(y1)
Problem 2. Find the general solution of the equation Note that one of two linearly independent solutions is yi(r) -e. Solution. Using Abel's formula, we get the following relations for the Wronskian dW pi dW 2r1 On the other hand, Comparing these two expression for W(x), we can take y2 :- r2yı. Correspondingly, the general solution is
Problem 2. Find the general solution of the equation Note...
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 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/...
a) Assume that y1(c) t and y2)te are solutions of the differential equation t2y_ t(t + 2))" + t(t + 2)y-0, t > 0 Do y1(t) and y2() form a fundamental set of solutions of the O.D.E.? C) State the general solution for this O.D.E.
a) Assume that y1(c) t and y2)te are solutions of the differential equation t2y_ t(t + 2))" + t(t + 2)y-0, t > 0 Do y1(t) and y2() form a fundamental set of solutions of...
Two solutions to y' + 6y + 25 = 0 are y1 = = e 3t sin(4t), y2 = e cos( 4t). a) Find the Wronskian. W b) Find the solution satisfying the initial conditions y(0) = - 4, y'(0) = 0 y =
yi 24 The joint probability function of Y1 and Y2 is given. 0 1/8 3/8 Y2 1 2/8 1/8 3 0 1/8 Find (a) Cov(Y1, Y2) and (b) the correlation coefficient p of Y, and Y2.
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-find the recurrence relation using power series
solutions.
2-find the first four terms in each of two solutions y1 and
y2
3-by evaluating wronskian w(y1,y2) show that they from a
fundamental solution set.
Iy yry 0, zo = 1
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