Question

Solve the differential equations in Problems 26 through 28 by regarding y as the independent variable rather than x. (x+yeʸ)

dy/dx =1

Answer 1

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.

1. Rearrange the differential equation to solve for dx/dy.
2. Integrate both sides with respect to y.
3. 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.