# Can someone just qickly check if this diff.equ is right?

• indie452
In summary, the problem involves evaluating the derivative of y with respect to x, given the equation dy/dx + y^2 + 1 = 0. The attempt at a solution involved finding an integrating factor and rearranging the equation to solve for y, but this solution did not hold true when plugged back into the original equation. The correct method is to rewrite the equation in a separable form and use an integrating factor to solve.

## Homework Statement

evaluate dy/dx + y2 + 1 = 0

## The Attempt at a Solution

dy/dx + y2 = -1

integtating factor I:- ex + c = exec = Cex

so xboth sides by I and rearranging forms:- d/dx(exy2) = -ex

integrating both sides:- exy2 = -ex + c

so y2 = -1 + Ce-x

y = SQRT[Ce-x -1]

With these kind of problems, like integrals it's really easy to check the answer yourself. Not only is it really easy, you really really should get used to doing it. Later on there won't be people to check your answers. Teaching yourself to be critical and able to convince yourself and others that your answer is correct is very important.

Plug the answer you got into the differential equation and you will see right away that the equality doesn't hold, thus your answer can't be right. I suggest you check this yourself and don't just take my word on it.

The correct way to do it is to write the differential equation as:

$$\frac{dy}{1+y^2}=-dx$$

Your equation, as previously noted, is separable. Integrating factors are used in functions of the form

$$y'(x) + P(x)y(x) = Q(x)$$

Where your integrating factor is $$\mu = e^{\int {P(x)dx} }$$