Final answer:
To solve the given differential equation and find the specific solution passing through the point (1,9), we can use different methods such as separation of variables or integrating factors.
Step-by-step explanation:
The given equation is a differential equation of the form dy/dx = 9x³ + 6e³ˣ + 3sin2x. To solve this differential equation, we need to find the function y(x) that satisfies this equation.
To solve this type of differential equation, we use different methods such as separation of variables, integrating factors, or homogeneous equations. In this case, we need to apply the appropriate method based on the form of the equation.
Given that the solution of the differential equation passes through the point (1,9), we can use this information to determine the specific solution by substituting the coordinates into the equation.