Write and then solve for y fx the differential equation for

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 y4.\"

Solution

y is a function of x and the rate of change of y with respect to x that is dy/dx is inversly proportional to y^4

=> the differential equation would be of the form :

dy/dx = C/y^4     , C is the constant of proportionality

y^(4)dy = Cdx

integrating both sides

=> integral y^4 dy = integral Cdx

y^5/5 = Cx + D

or y^5 = 5Cx + 5D

y^5 = Ex +F     , E and F are the constant of integration

Hence y = (Ex +F)^(1/5)