Question

Determine the longest interval in which the given initial value problem is certain to have a unique twice-differentiable solution. Do not attempt to find the solution. (Enter your answer using interval notation.) (x − 2)y'' + y' + (x − 2)(tan x)y = 0, y(3) = 1, y'(3) = 4

Answer 1

Answer:

answer in image. Thanks

Step-by-step explanation:

Answer 2

Discontinuous at x = 2

What is a differential equation?

The equation that is differentiable once or more than once is known as a differential equation.

How to solve?

$y'' + \frac{y'}{x-2} + \frac{(x-2)(tan x)y}{x-2} = 0\\y'' + \frac{y'}{x-2} +(tan x)y}= 0$

Differential equation is of type:

y'' + p(t)y' + q(t)y = g(t)

where p(t)  = $\frac{1}{x-2}$ , q(t) = tan x , g(t) = 0

point of discontinuity is at x = 2

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