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Example 0.3. Find all values of n for which y = ť" is a solution to...
Consider the system: 2 - 4x +y” = ť x' + 2 + y = 0...
Consider the system: 2 - 4x +y” = ť x' + 2 + y = 0 In the first blank: Write the second equation using the D notation. (Do not put any spaces in your answer) In the second blank: Solving the system, we get 2 c(t) = (use c1, c2 etc for our constants.) In the third blank: What is the form ofXp(t)? Wp = In the forth blank: What is the final form of the Ip(t) portion of...
evens from 2 and 6 In Exercises 1-6 find a particular solution by the method used...
evens from 2 and 6
In Exercises 1-6 find a particular solution by the method used in Example 5.3.2. Then find the general solution and, where indicated, solve the initial value problem and graph the solution. 1. y' + 5y - 6y= 22 + 180 - 1842 2. y' - 4y + 5y = 1+ 5.0 3. y' + 8y + 7y = -8-2+24x2 + 7ar3 4. y' - 4y + 4y = 2 + 8x - 4.2 CIG /'...
I need a solution to number 3 Find the solution to the initial value problem 2....
I need a solution to number 3
Find the solution to the initial value problem 2. y'+w+y=sin(nt), y(0) - 0, 0) = 0 where n is a positive integer and wan? What happens if w2 = n2? (Note that the right hand side has a form that works with Method of Undetermined Coefficients.) 3. y' + way = f(t), y(0) = 1, 10) = 0 l d where f(t) = {1-t, Ostal, -1-1+t, ist<2
Exercise 1: The Taylor series for In(y) about y = 1 is (4) In(y) = 9...
Exercise 1: The Taylor series for In(y) about y = 1 is (4) In(y) = 9 (-1)"+(v - 1) n=1 for y-1€ (-1,1] (that is, y E (0,2]). What polynomials do we get if we truncate this series at n = 1? n = 2? n = 0 (hint: the n = Oth approximation is defined!)? Compare the value of each of these with that of In(y) at y = 1.1 and y = 1.75. Note how the error differs...
(16 points) Consider the equation for the charge on a capacitor in an LRC circuit +...
(16 points) Consider the equation for the charge on a capacitor in an LRC circuit + 9 + 169 = E which is linear with constant coefficients. First we will work on solving the corresponding homogeneous equation. Divide through the equation by the coefficient on and find the auxiliary equation (using m as your variable) =0 which has roots The solutions of the homogeneous equation are Now we are ready to solve the nonhomogeneous equation +184 +809 = SE. We...
Use the backward Euler method with h = 0.1 to find approximate values of the solution...
Use the backward Euler method with h = 0.1 to find approximate values of the solution of the given initial value problem at t = 0.1, 0.2, 0.3 and 0.4. y' = 0.7 – + + 2y, y(O) = 2. Make all calculations as accurately as possible and round your final answers to two decimal places. In = nh n=1 0.1 n=2 0.2 n=3 0.3 n = 4 0.4
x < n with BCs y(0)= 0 and y(z) 0. (1 point) Find the eigenvalues and...
x < n with BCs y(0)= 0 and y(z) 0. (1 point) Find the eigenvalues and eigenfunctions for y" = Ay on 0 Note that any constant times an eigenfunction is also an eigenfunction. In order to obtain a unique solution find (x) so that x) dx 1 First find the eigenvalues and orthonormal eigenfunctions for n 1, i.e., An, >,(x). For n 0 there may or may not be an eigenpair. Give all these as a comma separated list....
My question is from the first step from where did we get 2 ? EXAMPLE 2.21...
My question is from the first step from where did we get 2 ?
EXAMPLE 2.21 FIRST-ORDER RECURSIVE SYSTEM (CONTINUED): COMPLETE SOLUTION Find the solution for the first-order recursive system described by the difference equation y[n] - Laxn – 1] = x[n] (2.46) if the input is x[n] = (1/2)*u[n] and the initial condition is y[ – 1] = 8. Solution: The form of the solution is obtained by summing the homogeneous solution determined in Example 2.18 with the particular...
This is the sequence 1,3,6,10,15 the pattern is addin 1 more than last time but what is the name for this pattern These are called the triangular numbers The sequence is 1 3=1+2 6=1+2+3 10=1+2+3+4 15=1+2+3+4+5 You can also observe this pattern
This is the sequence 1,3,6,10,15 the pattern is addin 1 more than last time but what is the name for this patternThese are called the triangular numbers The sequence is 1 3=1+2 6=1+2+3 10=1+2+3+4 15=1+2+3+4+5 You can also observe this pattern x _________ x xx __________ x xx xxx __________ x xx xxx xxxx to see why they're called triangular numbers. I think the Pythagoreans (around 700 B.C.E.) were the ones who gave them this name. I do know the...
forcast , time series question. (a) The values of the smoothing constants, a, y, and 8...
forcast , time series question.
(a) The values of the smoothing constants, a, y, and 8 for Holt-Winters method fall between 0 and 1. Explain what happens when each of them approaches or equals the values 0 and 1. (b) It has been found that quarterly sales of some sports drinks over 8 years has the multiplicative Holt-Winters optimum smoothing constants a=0.3, y = 0.1, and 8=0.2. It is also given that the final estimates for 131 = 168.1, 631...
Consider the system: 2 - 4x +y” = ť x' + 2 + y = 0 In the first blank: Write the second equation using the D notation. (Do not put any spaces in your answer) In the second blank: Solving the system, we get 2 c(t) = (use c1, c2 etc for our constants.) In the third blank: What is the form ofXp(t)? Wp = In the forth blank: What is the final form of the Ip(t) portion of...
evens from 2 and 6
In Exercises 1-6 find a particular solution by the method used in Example 5.3.2. Then find the general solution and, where indicated, solve the initial value problem and graph the solution. 1. y' + 5y - 6y= 22 + 180 - 1842 2. y' - 4y + 5y = 1+ 5.0 3. y' + 8y + 7y = -8-2+24x2 + 7ar3 4. y' - 4y + 4y = 2 + 8x - 4.2 CIG /'...
I need a solution to number 3
Find the solution to the initial value problem 2. y'+w+y=sin(nt), y(0) - 0, 0) = 0 where n is a positive integer and wan? What happens if w2 = n2? (Note that the right hand side has a form that works with Method of Undetermined Coefficients.) 3. y' + way = f(t), y(0) = 1, 10) = 0 l d where f(t) = {1-t, Ostal, -1-1+t, ist<2
Exercise 1: The Taylor series for In(y) about y = 1 is (4) In(y) = 9 (-1)"+(v - 1) n=1 for y-1€ (-1,1] (that is, y E (0,2]). What polynomials do we get if we truncate this series at n = 1? n = 2? n = 0 (hint: the n = Oth approximation is defined!)? Compare the value of each of these with that of In(y) at y = 1.1 and y = 1.75. Note how the error differs...
(16 points) Consider the equation for the charge on a capacitor in an LRC circuit + 9 + 169 = E which is linear with constant coefficients. First we will work on solving the corresponding homogeneous equation. Divide through the equation by the coefficient on and find the auxiliary equation (using m as your variable) =0 which has roots The solutions of the homogeneous equation are Now we are ready to solve the nonhomogeneous equation +184 +809 = SE. We...
Use the backward Euler method with h = 0.1 to find approximate values of the solution of the given initial value problem at t = 0.1, 0.2, 0.3 and 0.4. y' = 0.7 – + + 2y, y(O) = 2. Make all calculations as accurately as possible and round your final answers to two decimal places. In = nh n=1 0.1 n=2 0.2 n=3 0.3 n = 4 0.4
x < n with BCs y(0)= 0 and y(z) 0. (1 point) Find the eigenvalues and eigenfunctions for y" = Ay on 0 Note that any constant times an eigenfunction is also an eigenfunction. In order to obtain a unique solution find (x) so that x) dx 1 First find the eigenvalues and orthonormal eigenfunctions for n 1, i.e., An, >,(x). For n 0 there may or may not be an eigenpair. Give all these as a comma separated list....
My question is from the first step from where did we get 2 ?
EXAMPLE 2.21 FIRST-ORDER RECURSIVE SYSTEM (CONTINUED): COMPLETE SOLUTION Find the solution for the first-order recursive system described by the difference equation y[n] - Laxn – 1] = x[n] (2.46) if the input is x[n] = (1/2)*u[n] and the initial condition is y[ – 1] = 8. Solution: The form of the solution is obtained by summing the homogeneous solution determined in Example 2.18 with the particular...
forcast , time series question.
(a) The values of the smoothing constants, a, y, and 8 for Holt-Winters method fall between 0 and 1. Explain what happens when each of them approaches or equals the values 0 and 1. (b) It has been found that quarterly sales of some sports drinks over 8 years has the multiplicative Holt-Winters optimum smoothing constants a=0.3, y = 0.1, and 8=0.2. It is also given that the final estimates for 131 = 168.1, 631...
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