- #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)??