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>
Answer:
In the human body, cells are the basic units of life. Groups of cells working together for a specific function form tissues. Organs are two or more tissues operating together. Even separate organs work together, forming body systems.
Answer: Massive and Supermassive stars
Sensory nerves that are part of the peripheral nervous see your arm. Nerve impulses are brought to the brain by interneurons and the brain processes the information and you decide to lift your arm. Nerve impulses from the brain travel again through internuerons and into motor nerves that control the movement of your arm.