Question

x^2y'' − 3xy'+ 4y = 0 ; y(1)=5 y'(1)=3

differential equation using the Cauchy-Euler method

Answer #1

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

Solve the IVP with Cauchy-Euler ODE: x^2 y''+3xy'+4y=0; y(1)=0,
y’(1)=−2

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

X^2y’’ − 5xy’ + 8y = 8x^6; y(1/2) = 0; y’ (1/2) = 0
differential equation using the Cauchy-Euler method

Solve the following nonhomogenous Cauchy-Euler equations for x
> 0.
a. x^(2)y′′+3xy′−3y=3x^(2).

Consider the differential equation x^2y′′ − 3xy′ − 5y = 0. Note
that this is not a constant coefficient differential equation, but
it is linear. The theory of linear differential equations states
that the dimension of the space of all homogeneous solutions equals
the order of the differential equation, so that a fundamental
solution set for this equation should have two linearly fundamental
solutions.
• Assume that y = x^r is a solution. Find the resulting
characteristic equation for r....

Solve the following non homogenous Cauchy-Euler equations for x
> 0.
a. x2y′′+3xy′−3y=3x2.
b. x2y′′ −2xy′ +3y = 5x2, y(1) = 3,y′(1) =
0.

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)=

Use the substitution x = et to transform the given Cauchy-Euler
equation to a differential equation with constant coefficients.
(Use yp for dy /dt and ypp for d2y/dt2 .) x2y'' + 10xy' + 8y =
x2
Solve the original equation by solving the new equation using
the procedures in Sections 4.3-4.5. y(x) =

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

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