Question

X^2y’’ − 5xy’ + 8y = 8x^6; y(1/2) = 0; y’ (1/2) = 0

differential equation using the Cauchy-Euler method

Answer #1

Find the general solution to the Cauchy-Euler equation:
x^2 y'' - 5xy' + 8y = 0

x^2y'' − 3xy'+ 4y = 0 ; y(1)=5 y'(1)=3
differential equation using the Cauchy-Euler method

x^2y'' − 3xy'+ 4y = 0 ; y(1)=5 y'(1)=3
differential equation using the Cauchy-Euler method

In Exercises 1-20, find a general solution of the Cauchy-Euler
equation. (Assume x > 0).
2(x^(2))y''-8xy'+8y=0

Cauchy - Euler differential equation!!
(x^2)y" + xy' +4y = cos(2 ln(x)) what is the Cauchy -
Euler differential equation general solve?

Given the second-order differential equation
y''(x) − xy'(x) + x^2 y(x) = 0
with initial conditions
y(0) = 0, y'(0) = 1.
(a) Write this equation as a system of 2 first order
differential equations.
(b) Approximate its solution by using the forward Euler
method.

Find the general solution of the x ^ 3y '''- 8x ^ y''+ 28xy'-40y = -9 / x Cauchy-Euler differential equation.

Consider the following differential equation:
dydx=x+y
With initial condition: y = 1 when x = 0
Using the Euler forward method, solve this differential
equation for the range x = 0 to x = 0.5 in increments (step) of
0.1
Check that the theoretical solution is y(x) = - x -1 , Find the
error between the theoretical solution and the solution given by
Euler method at x = 0.1 and x = 0.5 , correct to three decimal
places

Solve the initial value problem below for the Cauchy-Euler
equation
t^2y"(t)+10ty'(t)+20y(t)=0, y(1)=0, y'(1)=2
y(t)=

Solve the given differential equation by undetermined
coefficients.
y'' + 2y' +-8y = xe2x

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