Consider the differential equation dy/dx = (y - y^2)/x.
1 answer:
We need to show that y = x/(x + c) is a solution of dy/dx = (y - y^2)/x. Then,
<span>dy/dx = ((x + c) * 1 - x * 1)/(x + c)^2 </span>
<span>= (x + c - x)/(x + c)^2 </span>
<span>= c/(x + c)^2 </span>
<span>and </span>
<span>(y - y^2)/x = (x/(x + c) - x^2/(x + c)^2)/x </span>
<span>= (x(x + c) - x^2)/(x(x + c)^2) </span>
<span>= (x^2 + cx - x^2)/(x(x + c)^2) </span>
<span>= cx/(x(x + c)^2) </span>
<span>= c/(x + c)^2 </span>
<span>which proves the equality. </span>
You might be interested in
Possibly a Great White or a DaggerNose
Number 3
Snnsbsbsbsnnsnsjsnensns didn’t
Yes plant cells do have mitochondira
the air and all the gasses
Are you talking about a fruit fly?
