Final answer:
To solve the differential equation (x + ye^y)dy/dx = 1 with y as the independent variable, we rearrange it to dx/dy = 1/(x + ye^y) and integrate with respect to y to find x as a function of y.
Step-by-step explanation:
The question asks us to solve the differential equation (x + ye^y)dy/dx = 1 by treating y as the independent variable. To do this, we first need to rearrange the equation and treat dx/dy as the element to be solved for, resulting in dx/dy = 1/(x + ye^y). We then integrate both sides with respect to y to find x as a function of y.
- Rearrange the differential equation to solve for dx/dy.
- Integrate both sides with respect to y.
- Find the general solution for x as a function of y.
If there are initial conditions given, we would then use them to find the particular solution.