Differential equations (derive general solutions)

[HUxv86]

I have two questions that I'm stumped on. I don't know where to start or how to finish them. My prof moves to fast for me. ANY help you can give would be great!!

#1 find the general solution of differential equation:
2xy^2 + x^2y' = y^2

#2 Each of the differential equations is of 2 different types considered ( seperable, linear, homogeneous, Bernoulli, exact, etc.) Derive general solutions for the equation in 2 different ways then reconcile your results.

dy/dx= xy^3 -xy

 

[Deleted member 4993]

I have two questions that I'm stumped on. I don't know where to start or how to finish them. My prof moves to fast for me. ANY help you can give would be great!!

#1 find the general solution of differential equation:
2xy^2 + x^2y' = y^2

This is a seperable variable problem.

x[supjyj9lj8]2[/supjyj9lj8] y' = y[supjyj9lj8]2[/supjyj9lj8] (1-2x)

y'/y[supjyj9lj8]2[/supjyj9lj8] = (1-2x)/x[supjyj9lj8]2[/supjyj9lj8]

Now continue....

#2 Each of the differential equations is of 2 different types considered ( seperable, linear, homogeneous, Bernoulli, exact, etc.) Derive general solutions for the equation in 2 different ways then reconcile your results.

dy/dx= xy^3 -xy

Try separable variable type first.
Please show your work, indicating exactly where you are stuck - so that we know where to begin to help you.