Question

Hi guys I wanted to know which one of these are seperable. and whats the equation and i want to do the rest please help out.

1) dy/dx = (xy+y)/4x-3xy)

2) dy/dx = y^2 +2x +3y

3) dy/dx = ye^(sinx + cosy)

Answer 1

If it's separable, it may be rearranged into this form
\[f(y)dy = g(x)dx\]

Answer 2

So nothing with x multiplies dy, and nothing with y multiplies dx.

Answer 3

yeah i know 3 is seperable i got that but i got confused by 1 and 2 the most

Answer 4

1 is separable.
\[\frac{xy+y}{4x-3xy}=\frac{y(x+1)}{x(4-3y)}=\frac{y}{4-3y}\cdot\frac{x+1}{x}\]