Question

Solve the IVP with Cauchy-Euler ODE: x^2 y''+ xy'−16y = 0; y(1) = 4, y'(1) = 0

Answer #1

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?

Solve the IVP: , y(0)=3.
2) Solve the DE: . y' = xy^2/ (x^2 +1)

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

In Exercises 1-20, find a general solution of the Cauchy-Euler
equation. (Assume x > 0).
4(x^(2))y''+17y=0

In Exercises 21-30, solve the nonhomogeneous Cauchy-Euler
equation. (Assume x > 0).
(x^(2))y''+2xy'-6y=2x

solve the Cauchy-Euler Initial value
9t2y''' + 15ty'+y= 0 with y(1) = 6 and y'(1) =1

Solve the ODE/ IVP
(y' + 1) = (x + y)^m / ((x + y)^n + (x + y)^p)
hint: z = x + y ; y' = z' - 1
Not sure how to start. Thanks in advance!

Consider ODE: (xy-1)dy+x^2dx=0.
Prove that φ (x, y) = 1/x it is an integrating factor.
Solve the ODE.

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)=

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