Final answer:
To find the value of k so that the given differential equation is exact, determine if the equation satisfies the condition for being exact by analyzing the mixed partial derivatives.
Step-by-step explanation:
To find the value of k so that the given differential equation is exact, you need to determine if the equation satisfies the condition for being exact. An exact differential equation is one where the total differential of the equation can be expressed as the partial derivatives of some function. You can check if the equation is exact by comparing the mixed partial derivatives and seeing if they are equal. If they are equal, you can solve for k.
For example, if the given differential equation is dx/dy + 2xy = k, you can calculate the mixed partial derivatives: ∂(∂f/∂x)/∂y = ∂(∂f/∂y)/∂x. If these derivatives are equal, the equation is exact. By determining and comparing these derivatives, you can then solve for k.