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

[indie452]

Homework Statement

evaluate dy/dx + y² + 1 = 0

The Attempt at a Solution

dy/dx + y² = -1

integtating factor I:- e^{x + c} = e^xe^c = Ce^x

so xboth sides by I and rearranging forms:- d/dx(e^xy²) = -e^x

integrating both sides:- e^xy² = -e^x + c

so y² = -1 + Ce^-x

y = SQRT[Ce^-x -1]

 

[Cyosis]

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:

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

 

[Pengwuino]

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 $$\mu = e^{\int {P(x)dx} }$$