Final answer:
The solution to the given differential equation is y = (x+2y³)e^C, where C is any constant.
Step-by-step explanation:
The differential equation given is (x+2y³) dy/ dx = y. To solve this equation, we can separate the variables and integrate both sides. Rearranging the equation gives us dy/y = dx/(x+2y³). Integrating both sides gives us ln|y| = ln|x+2y³| + C, where C is the constant of integration.
Next, we can exponentiate both sides to eliminate the natural logarithms. This gives us |y| = |x+2y³|e^C. Since e^C is a positive constant, we can remove the absolute value signs to obtain y = (x+2y³)e^C.
Therefore, the solution to the given differential equation is y = (x+2y³)e^C, where C is any constant.