Two differential equations How would I solve these differential equations? $$y'+2y^2=\frac{6}{x^2}$$ I tried finding integral product but couldn't find its integral. And also tried to trasform into homogen equation. and the second one is: $$xe^{2y}y'+e^{2y}=\frac{\ln x}{x}$$ How can I start? Thanks.

Well, I can figure out the second one. My guess was we could get the left side of the equation to look like

$$\frac d{dx}(f(x)e^{2y})=2f(x)e^{2y}y'+f'(x)e^{2y}$$

through the use of an integrating factor. So we have

$$\frac{f'(x)}{2f(x)}=\frac1x$$

$$\ln f(x)=2\ln x$$ $$f(x)=x^2$$

To get the equation into the proper form, multiply both sides by $2x$.

$$2x^2e^{2y}y'+2xe^{2y}=\frac d{dx}(x^2e^{2y})=2\ln x$$

I assume you can take this one from here?