Write and then solve for y = f(x) the differential equation for the statement: "The rate of change of y with respect to x is inversely proportional to y^4"
So dy/dx=k/y^4
(y^4)dy=(k)dx
Integrate
y^5/5=kx+C
Is this the final answer or is there more?
looks good to me.
or, you could say
y = 5kx+c
using a different c.
The expression you obtained, y^5/5 = kx + C, is indeed the solution to the differential equation you provided. However, it is always a good practice to check your answer and simplify it if possible.
To simplify the expression, you can multiply both sides of the equation by 5, resulting in y^5 = 5(kx + C). This yields the final simplified form of the equation.
Therefore, the final answer to the differential equation is y^5 = 5(kx + C).