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1. Compute et A for the following matrices, and write...
please be as neat as possible thank u Consider the differential equation X(1 — x)y" +...
please be as neat as possible thank u
Consider the differential equation X(1 — x)y" + [p – (p+ 2)x]y' – Py = 0, where p is a constant. (a) If p is not an integer, find the general solution near x = 0) in terms of Gauss's hypergeometric functions; Write the general solution found in (a) in terms of elementary functions;
Q2. Introduction to numerical methods Write out +1 explicitly in terms of r and n using Euler's m...
Q2. Introduction to numerical methods Write out +1 explicitly in terms of r and n using Euler's method, Improved Euler's method and RK4 method for the following differential equations (a) y, = t + ey (b) y" + ty'-logy = 0. Hint: Write it as a first order system then apply each method as vectors. Now consider for a constant λ < 0 L.e. the solution is y(t) and exponentially decays to zero. (c) Recall the general formula for yn...
XTAX=1. determine their canon- 1. Write the following quadratic forms as V(x) ical forms, find the modal matrices (i.e....
XTAX=1. determine their canon- 1. Write the following quadratic forms as V(x) ical forms, find the modal matrices (i.e. the matrices of unit eigenvectors) of the corresponding transformations and write down explicite expressions for canonical cOordinates (y1, 2, y3) in terms of the original coordinates (x1, X2, X3). State what surfaces these quadratic forms correspond to = > (a) x + 4x1r2 + 4a13-8a2x3 = 1; (b) a3a3a^ + 4xj2 +4x131223 1; (c) 4a7 2a2 2axjx2 2x13+ 6x23 = 1....
O Mo Tu We Th Fr Sa Su Memo No. Date Question 4 Consider the inhomogeneous...
O Mo Tu We Th Fr Sa Su Memo No. Date Question 4 Consider the inhomogeneous clifferential equation Ä + 5x+6X = Cost - 3 Sint and the associated homogeneous differential equation X+5x+6x=0 @ Formulate the characteristic equation and solve it 6 Hence write down the general Solution of the homogeneous differential equations @ Determine values of a and b such that Xple) = a cost +6 Sint is a particular Solution of the inhomogeneous differential equaliten @ Hence write...
1 Compute and completely factor the characteristic polynomial of the following matrix: 0 A= -4 5...
1 Compute and completely factor the characteristic polynomial of the following matrix: 0 A= -4 5 0 1 1 For credit, you have to factor the polynomial and show work for each step. B In the following, use complex numbers if necessary. For each of the following matrices: • compute the characteristic polynomial; • list all the eigenvalues (possibly complex) with their algebraic multiplicity; • for each eigenvalue, find a basis (possibly complex) of the corresponding eigenspace, and write the...
(1 point) In this problem we find the eigenfunctions and eigenvalues of the differential equation B+...
(1 point) In this problem we find the eigenfunctions and eigenvalues of the differential equation B+ iy=0 with boundary conditions (0) + (0) = 0 W2) = 0 For the general solution of the differential equation in the following cases use A and B for your constants, for example y = A cos(x) + B sin(x)For the variable i type the word lambda, otherwise treat it as you would any other variable. Case 1: 1 = 0 (1a.) Ignoring the...
PLEASE ANSWER ALL PARTS OF THE QUESTION Problem III (20 points) Consider the following Euler's equation...
PLEASE ANSWER ALL PARTS OF THE QUESTION
Problem III (20 points) Consider the following Euler's equation tx" – 2tx' + 2x = 3t”, t > 0. 1. (5 points) Make a substitution and write down the equivalent differential equation after the substitution. 2. (10 points) Find the general solution for the differential equation you write down in the previous question. 3. (5 points) Find the solution z(t) such that x(1) = 0, x'(1) = 0
Hi! I need help with this college level differential equations question. Please show all work and...
hi! I need help with this
college level differential equations question. Please show all work
and thank you.
3. We will next use matrix exponentials to find a fundamental matrix for the given system of DEs, (t) = P3(t) , P= (a) Letỉ(t) Ty(t), where Ț s a 2 2 constant matrix. Then, the system becomes = Dy, where D-T-1 PT. Find matrices T and D, such that D is a diagonal matrix. (Note that D and T are complex...
n=7 Question 4 5 pts Consider the equation nº X" () + X(T) - 0 with...
n=7
Question 4 5 pts Consider the equation nº X" () + X(T) - 0 with the following boundary conditions. X(0) + X'(0) -0, and X(n) + X'(n) - 0. 1. Write down the general solution to the equation for XC). 2. Write down the result of applying the boundary condition X(0) + X'(0) = 0 to the general solution 3. Write down the result of applying the remaining boundary condition X(n) - X'(n) = ( to the general solution....
n=5 Question 4 5 pts Consider the equation nº X" () + X(T) - 0 with...
n=5
Question 4 5 pts Consider the equation nº X" () + X(T) - 0 with the following boundary conditions. X(0) + X'(0) -0, and X(n) + X'(n) - 0. 1. Write down the general solution to the equation for XC). 2. Write down the result of applying the boundary condition X(0) + X'(0) = 0 to the general solution 3. Write down the result of applying the remaining boundary condition X(n) - X'(n) = ( to the general solution....
please be as neat as possible thank u
Consider the differential equation X(1 — x)y" + [p – (p+ 2)x]y' – Py = 0, where p is a constant. (a) If p is not an integer, find the general solution near x = 0) in terms of Gauss's hypergeometric functions; Write the general solution found in (a) in terms of elementary functions;
Q2. Introduction to numerical methods Write out +1 explicitly in terms of r and n using Euler's method, Improved Euler's method and RK4 method for the following differential equations (a) y, = t + ey (b) y" + ty'-logy = 0. Hint: Write it as a first order system then apply each method as vectors. Now consider for a constant λ < 0 L.e. the solution is y(t) and exponentially decays to zero. (c) Recall the general formula for yn...
XTAX=1. determine their canon- 1. Write the following quadratic forms as V(x) ical forms, find the modal matrices (i.e. the matrices of unit eigenvectors) of the corresponding transformations and write down explicite expressions for canonical cOordinates (y1, 2, y3) in terms of the original coordinates (x1, X2, X3). State what surfaces these quadratic forms correspond to = > (a) x + 4x1r2 + 4a13-8a2x3 = 1; (b) a3a3a^ + 4xj2 +4x131223 1; (c) 4a7 2a2 2axjx2 2x13+ 6x23 = 1....
O Mo Tu We Th Fr Sa Su Memo No. Date Question 4 Consider the inhomogeneous clifferential equation Ä + 5x+6X = Cost - 3 Sint and the associated homogeneous differential equation X+5x+6x=0 @ Formulate the characteristic equation and solve it 6 Hence write down the general Solution of the homogeneous differential equations @ Determine values of a and b such that Xple) = a cost +6 Sint is a particular Solution of the inhomogeneous differential equaliten @ Hence write...
1 Compute and completely factor the characteristic polynomial of the following matrix: 0 A= -4 5 0 1 1 For credit, you have to factor the polynomial and show work for each step. B In the following, use complex numbers if necessary. For each of the following matrices: • compute the characteristic polynomial; • list all the eigenvalues (possibly complex) with their algebraic multiplicity; • for each eigenvalue, find a basis (possibly complex) of the corresponding eigenspace, and write the...
(1 point) In this problem we find the eigenfunctions and eigenvalues of the differential equation B+ iy=0 with boundary conditions (0) + (0) = 0 W2) = 0 For the general solution of the differential equation in the following cases use A and B for your constants, for example y = A cos(x) + B sin(x)For the variable i type the word lambda, otherwise treat it as you would any other variable. Case 1: 1 = 0 (1a.) Ignoring the...
PLEASE ANSWER ALL PARTS OF THE QUESTION
Problem III (20 points) Consider the following Euler's equation tx" – 2tx' + 2x = 3t”, t > 0. 1. (5 points) Make a substitution and write down the equivalent differential equation after the substitution. 2. (10 points) Find the general solution for the differential equation you write down in the previous question. 3. (5 points) Find the solution z(t) such that x(1) = 0, x'(1) = 0
hi! I need help with this
college level differential equations question. Please show all work
and thank you.
3. We will next use matrix exponentials to find a fundamental matrix for the given system of DEs, (t) = P3(t) , P= (a) Letỉ(t) Ty(t), where Ț s a 2 2 constant matrix. Then, the system becomes = Dy, where D-T-1 PT. Find matrices T and D, such that D is a diagonal matrix. (Note that D and T are complex...
n=7
Question 4 5 pts Consider the equation nº X" () + X(T) - 0 with the following boundary conditions. X(0) + X'(0) -0, and X(n) + X'(n) - 0. 1. Write down the general solution to the equation for XC). 2. Write down the result of applying the boundary condition X(0) + X'(0) = 0 to the general solution 3. Write down the result of applying the remaining boundary condition X(n) - X'(n) = ( to the general solution....
n=5
Question 4 5 pts Consider the equation nº X" () + X(T) - 0 with the following boundary conditions. X(0) + X'(0) -0, and X(n) + X'(n) - 0. 1. Write down the general solution to the equation for XC). 2. Write down the result of applying the boundary condition X(0) + X'(0) = 0 to the general solution 3. Write down the result of applying the remaining boundary condition X(n) - X'(n) = ( to the general solution....
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