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.
(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, 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.
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
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.
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 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...