Question

In: Advanced Math

A laguerre equation is any differential equation of the form xy"+(1-x)y'+ny=0 where n is an integer....

A laguerre equation is any differential equation of the form xy"+(1-x)y'+ny=0 where n is an integer. Solve the Laguerre equation with n = 1, that is solve xy"+(x-1)y'+y=0 about the singlular point x=0.

Solutions

Expert Solution


Related Solutions

Find the general power series solution for the differential equation 2x^2y''-xy'+(x^2 +1) y =0 about x=0...
Find the general power series solution for the differential equation 2x^2y''-xy'+(x^2 +1) y =0 about x=0 (Answer should be given to the x^4+r term)
(Differential Equations) Consider the differential equation xy’-x4y3+y=0 Verify that the function y = (Cx2-x4)-1/2 is a...
(Differential Equations) Consider the differential equation xy’-x4y3+y=0 Verify that the function y = (Cx2-x4)-1/2 is a solution of the differential equation where C is an arbitrary constant. Find the value of C such that y(-1) = 1. State the solution of the initial value problem. State the interval of existence.
Power series Find the particular solution of the differential equation: (x^2+1)y"+xy'-4y=0 given the boundary conditions x=0,...
Power series Find the particular solution of the differential equation: (x^2+1)y"+xy'-4y=0 given the boundary conditions x=0, y=1 and y'=1. Use only the 7th degree term of the solution. Solve for y at x=2. Write your answer in whole number.
Find the general solution to the differential equation. y'=xy/x−4 y(x)=C⋅ ...
Find the general solution to the differential equation. y'=xy/x−4 y(x)=C⋅ ...
Consider the differential equation x′=[2 4 -2 −2], with x(0)=[1 1] Solve the differential equation where...
Consider the differential equation x′=[2 4 -2 −2], with x(0)=[1 1] Solve the differential equation where x=[x(t)y(t)]. x(t)= y(t)= please be as clear as possible especially when solving for c1 and c2 that's the part i need help the most
Find the series solution to the following differential equation: y" + xy' - y = x^2...
Find the series solution to the following differential equation: y" + xy' - y = x^2 - 2x , about x = 1
Consider the differential equation: y'(x)+3xy+y^2=0.     y(1)=0.    h=0.1 Solve the differential equation to determine y(1.3) using: a....
Consider the differential equation: y'(x)+3xy+y^2=0.     y(1)=0.    h=0.1 Solve the differential equation to determine y(1.3) using: a. Euler Method b. Second order Taylor series method c. Second order Runge Kutta method d. Fourth order Runge-Kutta method e. Heun’s predictor corrector method f. Midpoint method
Let f(x) = {(C/x^n if 1≤ x <∞; 0 elsewhere)} where n is an integer >1....
Let f(x) = {(C/x^n if 1≤ x <∞; 0 elsewhere)} where n is an integer >1. a. Find the value of the constant C (in terms of n) that makes this a probability density function. b. For what values of n does the expected value E(X) exist? Why? c. For what values of n does the variance var(X) exist? Why?
5. Consider the differential equation xy^5/2 +1+x^2y^3/2dy/dx =0 (a) Show that this differential equation is not...
5. Consider the differential equation xy^5/2 +1+x^2y^3/2dy/dx =0 (a) Show that this differential equation is not exact. (b) Find a value for the constant a such that, when you multiply the d.e. through by xa, it becomes exact. Show your working. Do NOT solve the resulting differential equation. 6. Consider the differential equation (D − 3)(D − 4)y = 0. (a) Solve this d.e., showing brief working. (b) How many solutions does this d.e. have? Justify your answer. (c) How...
Solve the differential equation 1. a) 2xy"+ y' + y = 0 b) (x-1)y'' + 3y...
Solve the differential equation 1. a) 2xy"+ y' + y = 0 b) (x-1)y'' + 3y = 0
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT