please be clear on all steps 4. Consider the differential operator L given by: L =...
Only the last one please
Consider the following initial value problem to be solved by undetermined coefficients. y" - 36 = 9, y(0) = 1, YO) = 0 Write the given differential equation in the form L(y) = g(x) where L is a linear operator with constant coefficients. If possible, factor L. (Use D for the differential operator.) (\(D-6) (D+6) Jy = 16 Find a linear differential operator that annihilates the function g(x) = 16. (Use D for the differential...
Find the eigenvalues and
eigenfunctions for the differential operator L(y)=−y″L(y)=−y″ with
boundary conditions y′(0)=0y′(0)=0 and y′(3)=0y′(3)=0, which is
equivalent to the following BVP
y″+λy=0,y′(0)=0,y′(3)=0.y″+λy=0,y′(0)=0,y′(3)=0.
Find the eigenvalues and eigenfunctions for the differential operator L(y)--y" with boundary conditions y (0)0 and y' (3)-0, which is equivalent to the following BVP (a) Find all eigenvalues 2n as function of a positive integer n > 1. (b) Find the eigenfunctions yn corresponding to the eigenvaluesn found in part (a). Help Entering Answers ew...
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Find the eigenvalues given the Eigen functions and operators Operator: the hydrogen atom Hamiltonian -h^2/2m {1/r^2 partial differential/ partial differential r (r^2) partial differential Psi(r, theta, phi )/ partial differential r + 1/r^2 sin(theta) partial differential / partial differential theta sin(theta) partial differential Psi (r, theta phi)/ partial differential theta + 1/r^2 sin^2 (theta) partial differential^2 Psi(r, theta, phi)/ partial differential phi ^2 } Ze^2/4 pi epsilon_0 r Psi(r, theta, phi) = E Psi(r, theta, phi) Eigen...
Answer ALL the questions. Some or all of them shall be marked. Question 1. Consider the following system of differential equations: P.(D) [x] + P (D)) -(0) Px(D) [x] + P (D) x = f(t). (1) How do we determine the correct number of arbitrary constants in a general solution of the above system. (0) Explain briefly the difference between the operator method and the method of triangu- larization when used for solving the above system. Question 2. Determine whether...
Consider the following second order linear operator: 82 with Notice, that if instead of 3 we had 2 there, we would get a Legendre operator (whose eigenfunctions are Legendre polynomials). But nothing can be further from it than the operator above. The eigenvalue/eigenfunction problem, emerged in the analysis of vibrations of a particular quant urn liquid. An eigenvalue λ corresponds to an excitation mode of frequency Ω = V The eigenfunction ψ(r) would give a spatial profile of the deviation...
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please with clear font
this is a differential equation question please solve them with steps and details also make sure it is correct 4. (7 points) Consider the following system of differential equations, solve it using both the direct method and the Decoupling Method, and compare your results from both methods. T 3r - 2y y -x+y+32
Solve it please
Find a linear differential operator that annihilates the given function. (Use D for the differential operator.) 9x – sin(x) + 14 cos(7x)
please solve all 3 Differential Equation problems
3.8.7 Question Help Consider the following eigenvalue problem for which all of its eigenvalues are nonnegative y',thy-0; y(0)-0, y(1) + y'(1)-0 (a) Show that λ =0 is not an eigenvalue (b) Show that the eigenfunctions are the functions {sin α11,o, where αη įs the nth positive root of the equation tan z -z (c) Draw a sketch indicating the roots as the points of intersection of the curves y tan z and y...
Find linearly independent functions that are annihilated by the given differential operator. (Give as many functions as possible. Use x as the independent variable. Enter your answers as a comma-separated list.) 1. D4 2. D2 − 7D − 44 Solve the given initial-value problem: 2. y'' + y = 10 cos 2x − 4 sin x, y(π/2) = −1, y'(π/2) = 0 : y(x)=____________
Given y'"- y" - 4y'- 6y=0 (1) , identify Differential Operator L of (1). OL=D3-D2 - 4D - 6 o L = (D - 3)(D2 + 2D + 2) O Both of them are correct! None of them