Final answer:
The general (explicit) solution to the given differential equation dy/dx = y⁴cos x is represented by Yk(x) = Ak cos kx + Bk sin kx, where Ak and Bk are constants and k is a parameter.
Step-by-step explanation:
The general (explicit) solution to the given differential equation dy/dx = y⁴cos x is represented by Yk(x) = Ak cos kx + Bk sin kx, where Ak and Bk are constants and k is a parameter.
This solution is obtained by substituting Yk(x) into the differential equation and solving for the constants Ak and Bk. The resulting solution represents a family of solutions that satisfy the given differential equation.
By varying the values of the constants Ak, Bk, and the parameter k, we can obtain different specific solutions within the general solution.