- #1

Rijad Hadzic

- 321

- 20

## Homework Statement

Find the general solution of the given differential equation. Give the largest interval I over which the interval is defined.Determine wether there are any transient terms in the general solution11.

[itex] x\frac {dy}{dx} - y = x^2sin(x)[/itex]

## Homework Equations

## The Attempt at a Solution

[itex] \frac {dy}{dx} + x^{-1}y = sin(x) [/itex]

[itex] e^{-\int {x^{-1} dx }} = 1/x [/itex]

[itex] d/dx[yx^{-1}] = sin(x) [/itex]

[itex] yx^{-1} = -cos(x) + c [/itex]

[itex] y = -xcos(x) + cx [/itex]

I don't understand why the interval of solution isn't (-inf, inf), as that would be the largest solution. My book says its (0,inf)

How could zero not be included?

Why would the interval of solution be (0,inf)? Couldn't (-inf,inf) be a solution as well? Because even if x = 0, you simply get -(0)(1) + c(0) = 0, which is a real number, so why can't it be (-inf,inf)??