Homework Soursedydxky1yL turns into L1bekt Find the equation for dXdt3X5 x2
dy/dx=ky(1-y/L) turns into L/(1+be^(-kt)
Find the equation for dX/dt=(3X/5) -x^(2)/350 (0,5)
Find the equation for dX/dt=(3X/5) -x^(2)/350 (0,5)
Solution
dy/dt =ky(1-y/L) has a soln y=L/(1+be^(-kt)) (given) Now, dx/dt = 3x/5-x^2/350 =(210x-x^2)/350 =[x(210-x)]/350 =[210x(1-x/210)]/350 =(3/5)x(1-x/210) Comparing with given equation, we have k=3/5, L=210 Hence, the solution is x=210/(1+be^(-3t/5)) If (0,5) means that X=5 at t=0, we have, 5=210/(1+be^0) or, 1+b=210/5=42 or, b=41 So, x=210/(1+41e^(-3t/5))
