Final answer:
The general solution to the given differential equation yʹ = sin(x)ecos(x) can be found by integrating both sides of the equation. The general solution is y = -sin(x) + C - ecos(x), where C is the constant of integration.
Step-by-step explanation:
The general solution to the given differential equation yʹ = sin(x)ecos(x) can be found by using the method of integration. First, we integrate both sides of the equation with respect to x. The integral of sin(x)ecos(x) with respect to x can be found using integration by substitution. Once the integral is found, we can add a constant of integration to obtain the general solution.
Therefore, the general solution to the differential equation is: y = -sin(x) + C - ecos(x), where C is the constant of integration.