Final answer:
To solve the differential equation (dy)/(dx)=y³cos(x), use separation of variables and integrate both sides. The general solution is y² = -1/(2sin(x) + 2C).
Step-by-step explanation:
To solve the differential equation (dy)/(dx)=y³cos(x), we can use separation of variables. Rearrange the equation to get dy/y³ = cos(x)dx. Integrate both sides: ∫(dy/y³) = ∫cos(x)dx.
To solve the differential equation (dy)/(dx)=y³cos(x), use separation of variables and integrate both sides. The general solution is y² = -1/(2sin(x) + 2C).
This gives us (-1/2y²) = sin(x) + C, where C is an arbitrary constant. So, the general solution to the differential equation is y² = -1/(2sin(x) + 2C).