Given: x2y"+5xy'+4y=0 Find y(2) given that the 2 arbitrary constants are equal and each has a...
(1 point) Find the solution of x2y" + 5xy + (4 + 3x)y = 0, x > 0 of the form Yi = x" Ž Cpx”, n=0 where co = : 1. Enter r = Cn = n = 1,2,3,...
Given a second order linear homogeneous differential equation a2(x)” + a (x2y + a)(x2y = 0 we know that a fundamental set for this ODE consists of a pair linearly independent solutions yı, y. But there are times when only one function, call it yi, is available and we would like to find a second linearly independent solution. We can find y2 using the method of reduction of order. First, under the necessary assumption the az(x) + 0 we rewrite...
For the following Euler-Cauchy equation: x2y" + axy + by = 0 a) Show that y(x)-xrnis a solution where mis equal to m -(1-a) | (1-а)2-b b) Show that for the case when ^1 -a)2 - b 0, the general solution is equal to 4. 4 1-a y(x) = x-2-(G + c2 In x) c) Solve the following problem x2y"-5xy' + 9y-0, y(1)-0.2, y'(1)-0.3 d) Show that for the case when-(1-a)2-b 〈 0, the general solution is equal to 1-а...
Verify that the given function is a solution to the given
differential equation (c1 and c2 are arbitrary constants), and
state the maximum interval over which the solution is valid.
14. y(x) = cix-3 + c2x-1, x2y" + 5xy' + 3y = 0.
Problem #8: Find the eigenfunctions for the following boundary value problem. x2y"-19xy(100 A)y = 0. y(e) = 0, y(1) = 0. In the eigenfunction take the arbitrary constant (either c1 or c) from the general solution to be 1 Enter your answer as a symbolic function of x.n, as in these examples Problem #8: Do not include 'yin your answer.
Problem #8: Find the eigenfunctions for the following boundary value problem. x2y"-19xy(100 A)y = 0. y(e) = 0, y(1) =...
Consider the following boundary value problem,
x2y′′ + 17xy′ + (64 +
λ) y = 0, y(1)
= 0, y(e6 ) = 0
(a)
Find the eigenvalues.
(b)
Find the eigenfunctions. Take the arbitrary constant (either
c1 or c2) from the general
solution to be 1.
Consider the following boundary value problem, xy" + 17xy' + (64 + 2) y = 0, y(1) = 0, yle) = 0 (a) Find the eigenvalues. (b) Find the eigenfunctions. Take the arbitrary constant (either...
For the differential equation y" + 4y' + 13y = 0, a general solution is of the form y = e-2x(C1sin 3x + C2cos 3x), where C1 and C2 are arbitrary constants. Applying the initial conditions y(0) = 4 and y'(0) = 2, find the specific solution. y = _______
consider the DE: y''+x2y'+x2y=0 about the ordinary point x=0 a) find the recurrence relation, and indicate if any of the coefficients are equal to zero .(if any) b) use the recurrence relation to write the first four nonzero terms of each of the two linearly independent power series near the ordinary point x=0. My attempt... after plugging in the y, y' , and y'' power series. I got something that looked like 2a2+6a3x + sigma from n=2 -> to infinity...
The general solution of the Cauchy-Euler differential equation x’y" + 5xy' + 4y = 0 is a) y = ce-* + c2e-4x b) y = c;e-2x + czxe-2x d) y = Cyx-2 + c2x-2 Inx c) y = C1x-1 + c2x Select one: C a
Solve the given differential equations:
х 1. y' = y(0) = -2 y+x2y 2. 3x²y dx – (x3 + y3)dy = 0 , y(1) = -2