Question

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."

Answer 1

dy/dx = k / y^4

Answer 2

Wouldn't it be x / y^4?

Answer 3

no ,it is inversely proportional y^4 only.

Answer 4

So how would I solve it?

Answer 5

\[\sqrt[5]{5x^2/2+C}\]?

Answer 6

But with a 'k' for 'x'?

Answer 7

y^4dy=kdx
integrate both sides
\[\frac{ y^5 }{ 5 }=kx+c\]