Final answer:
To find the general solution to the differential equation dy/dx = 3x(x-1), integrate the right-hand side with respect to x, which after applying the power rule, yields the general solution y = x^3 - (3/2)x^2 + C.
Step-by-step explanation:
The student is asked to use integration to find the general solution to the differential equation dy/dx = 3x(x-1). To solve this, we integrate the right-hand side of the equation with respect to x to find y.
- Write down the differential equation: dy/dx = 3x(x - 1).
- Integrate the right-hand side with respect to x: \(∫y dx = \int 3x^2 - 3x dx\).
- Apply the power rule of integration to each term: y = x^3 - (3/2)x^2 + C, where C is the constant of integration.
The general solution to the differential equation is then y = x^3 - (3/2)x^2 + C.