Final answer:
To determine if the given differential equation is exact, we need to check if the partial derivatives of the function with respect to x and y are equal. If they are, we can solve it using the exact solution method. In this case, the equation is not exact, so it requires a different approach.
Step-by-step explanation:
We have to determine whether the given differential equation is exact and if it is, solve it. The differential equation is 1 + ln(x) + y/x dx = (3 − ln(x)) dy. To check if it is exact, we need to verify if the partial derivatives of the function with respect to x and y are equal.
Taking the partial derivative of (1 + ln(x) + y/x) with respect to x gives 1/x. Taking the partial derivative of (3 − ln(x)) with respect to y gives 0. Since 1/x is not equal to 0, the equation is not exact.
Therefore, we cannot solve it using the exact solution method. It requires a different approach beyond the scope of this course.