- #1

Rijad Hadzic

- 321

- 20

## Homework Statement

For a differential equation I have solution

y= (1/3) + ce^(-x^3) where c is a constant

The interval of solution is (-inf,inf)

that makes sense to me, since e^x never has a value of y that equals zero.

Edit: this is the original question:

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 solution

5.

[itex] \frac {dy}{dx} + 3x^2y = x^2 [/itex]

[itex] e^{\int {3x^2 dx}} [/itex] -->>> [itex] e^{x^3} [/itex]

[itex] e^{x^3} y = \int {e^{x^3}x^2 } [/itex]

[itex] y = (1/3) + ce^{-x^3} [/itex]

## Homework Equations

## The Attempt at a Solution

It makes sense when you look at a graph of e^x... but if I set e^(x^3) = 0, and I take ln for both side, and get x = ln(0)^(1/3)

wouldn't ln(0)^(1/3) be a number, and that number make the function undefined?

I'm trying to understand why it makes sense graphically but doesn't make sense logically.

My reasoning would be as follows: there is not an x value for ln(0)^1/3.

Meaning, if you look on the number line, no value of ln(0)^1/3 exists in the domain.

This reasoning makes sense to me but I feel like I'm not grasping the whole picture... can anyone help me out by clarifying? Can anyone help me out by pointing any faulty statements out? Again I thank you guys.

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