Final answer:
To solve the separable differential equation dy/dx = x², integrate both sides to obtain y = (1/3)x³ + C, where C is the constant of integration.
Step-by-step explanation:
To solve the separable differential equation dy/dx = x², you can integrate both sides of the equation. This can be done by separating the variables, which means rewriting the equation so that all y terms are on one side and all x terms are on the other:
- Integrate dy = x² dx.
- ∫ dy = ∫ x² dx.
- y = (1/3)x³ + C, where C is the constant of integration.
The solution to the differential equation is y = (1/3)x³ + C.