Can Non-Linear Separable Differential Equations Be Solved?

[EtherealMonkey]

Homework Statement

$$\frac{dy}{dx}+2xy^{2}=0$$

I am stuck on this.

I realize that this is a non-linear exact equation, but I just cannot wrap my mind around any type of method to attack this one.

TIA for any help

 

[LCKurtz]

You noticed it is separable, so just separate the variables.

 

[EtherealMonkey]

Okay, never-mind...

Problem:

$$\frac{dy}{dx}+2xy^{2}=0$$

Solution:

$$\frac{dy}{dx}=-\left(2xy^{2}\right)$$

$$\left(\frac{1}{y^{2}}\right)\frac{dy}{dx}=-2x$$

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

$$y=\frac{1}{x^{2}+C_{1}}$$

 

[EtherealMonkey]

You noticed it is separable, so just separate the variables.

Yeah, my CalIII is killing me...

Thanks for the response. I hope the next time I have a question, it will be a good one